mnist.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xLOXFOT5Q40E"
   },
   "source": [
    "##### Copyright 2020 The TensorFlow Authors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "iiQkM5ZgQ8r2",
    "tags": []
   },
   "outputs": [],
   "source": [
    "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "j6331ZSsQGY3"
   },
   "source": [
    "# MNIST classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "i9Jcnb8bQQyd"
   },
   "source": [
    "Based on https://www.tensorflow.org/quantum/tutorials/mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "udLObUVeGfTs"
   },
   "source": [
    "We build a quantum neural network (QNN) to classify a simplified version of MNIST, similar to the approach used in <a href=\"https://arxiv.org/pdf/1802.06002.pdf\" class=\"external\">Farhi et al</a>. The performance of the quantum neural network on this classical data problem is compared with a classical neural network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "X35qHdh5Gzqg"
   },
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "TorxE5tnkvb2",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n",
      "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
      "tfq-nightly 0.5.0.dev20210516 requires grpcio==1.30.0, but you have grpcio 1.32.0 which is incompatible.\u001b[0m\n",
      "\u001b[33mWARNING: You are using pip version 21.1.1; however, version 21.1.2 is available.\n",
      "You should consider upgrading via the '/mnt/c/Users/mmints/Documents/Stanford/CS230/project/CS230_quantum_dropout/qenv_project/bin/python3.8 -m pip install --upgrade pip' command.\u001b[0m\n",
      "Requirement already satisfied: tensorboard_plugin_profile==2.3.0 in ./qenv_project/lib/python3.8/site-packages (2.3.0)\n",
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      "\u001b[33mWARNING: You are using pip version 21.1.1; however, version 21.1.2 is available.\n",
      "You should consider upgrading via the '/mnt/c/Users/mmints/Documents/Stanford/CS230/project/CS230_quantum_dropout/qenv_project/bin/python3.8 -m pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "%reset\n",
    "\n",
    "#!pip3 install -q tensorflow==2.3.1\n",
    "!python3.8 -m pip install -q tensorflow==2.4.1\n",
    "!python3.8 -m pip install tensorboard_plugin_profile==2.3.0\n",
    "%load_ext tensorboard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FxkQA6oblNqI"
   },
   "source": [
    "Install TensorFlow Quantum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "saFHsRDpkvkH",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Installing collected packages: grpcio\n",
      "  Attempting uninstall: grpcio\n",
      "    Found existing installation: grpcio 1.32.0\n",
      "    Uninstalling grpcio-1.32.0:\n",
      "      Successfully uninstalled grpcio-1.32.0\n",
      "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
      "tensorflow 2.4.1 requires grpcio~=1.32.0, but you have grpcio 1.30.0 which is incompatible.\u001b[0m\n",
      "Successfully installed grpcio-1.30.0\n",
      "\u001b[33mWARNING: You are using pip version 21.1.1; however, version 21.1.2 is available.\n",
      "You should consider upgrading via the '/mnt/c/Users/mmints/Documents/Stanford/CS230/project/CS230_quantum_dropout/qenv_project/bin/python3.8 -m pip install --upgrade pip' command.\u001b[0m\n",
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     ]
    },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARNING: You are using pip version 21.1.1; however, version 21.1.2 is available.\n",
      "You should consider upgrading via the '/mnt/c/Users/mmints/Documents/Stanford/CS230/project/CS230_quantum_dropout/qenv_project/bin/python3.8 -m pip install --upgrade pip' command.\u001b[0m\n",
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      "\u001b[33mWARNING: You are using pip version 21.1.1; however, version 21.1.2 is available.\n",
      "You should consider upgrading via the '/mnt/c/Users/mmints/Documents/Stanford/CS230/project/CS230_quantum_dropout/qenv_project/bin/python3.8 -m pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "#!pip3 install -q tensorflow-quantum\n",
    "!python3.8 -m pip install tfq-nightly\n",
    "\n",
    "\n",
    "!python3.8 -m pip install scikit-image\n",
    "!python3.8 -m pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hdgMMZEBGqyl"
   },
   "source": [
    "Now import TensorFlow and the module dependencies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "enZ300Bflq80",
    "tags": []
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow_quantum as tfq\n",
    "\n",
    "import cirq\n",
    "import sympy\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import collections\n",
    "import datetime\n",
    "# visualization tools\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from cirq.contrib.svg import SVGCircuit\n",
    "from skimage.util import random_noise\n",
    "\n",
    "# set the random seed\n",
    "tf.random.set_seed(137)\n",
    "np.random.seed(137)\n",
    "\n",
    "\n",
    "\n",
    "NUM_EXAMPLES = 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "b08Mmbs8lr81"
   },
   "source": [
    "## 1. Load the data\n",
    "\n",
    "In this tutorial you will build a binary classifier to distinguish between the digits 3 and 6, following <a href=\"https://arxiv.org/pdf/1802.06002.pdf\" class=\"external\">Farhi et al.</a> This section covers the data handling that:\n",
    "\n",
    "- Loads the raw data from Keras.\n",
    "- Filters the dataset to only 3s and 6s.\n",
    "- Downscales the images so they fit can fit in a quantum computer.\n",
    "- Removes any contradictory examples.\n",
    "- Converts the binary images to Cirq circuits.\n",
    "- Converts the Cirq circuits to TensorFlow Quantum circuits. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pDUdGxn-ojgy"
   },
   "source": [
    "### 1.1 Load the raw data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xZyGXlaKojgz"
   },
   "source": [
    "Load the MNIST dataset distributed with Keras. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "d9OSExvCojg0",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of original training examples: 60000\n",
      "Number of original test examples: 10000\n"
     ]
    }
   ],
   "source": [
    "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()\n",
    "\n",
    "# Rescale the images from [0,255] to the [0.0,1.0] range.\n",
    "x_train, x_test = x_train[..., np.newaxis]/255.0, x_test[..., np.newaxis]/255.0\n",
    "\n",
    "print(\"Number of original training examples:\", len(x_train))\n",
    "print(\"Number of original test examples:\", len(x_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fZpbygdGojg3"
   },
   "source": [
    "Filter the dataset to keep just the 3s and 6s,  remove the other classes. At the same time convert the label, `y`, to boolean: `True` for `3` and `False` for `5`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "hOw68cCZojg4",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def filter_35(x, y):\n",
    "    keep = (y == 3) | (y == 5)\n",
    "    x, y = x[keep], y[keep]\n",
    "    y = y == 3\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "p-XEU8egGL6q",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of filtered training examples: 11552\n",
      "Number of filtered test examples: 1902\n",
      "0.3\n",
      "0.7\n",
      "After restricting - number of filtered training examples: 500\n",
      "After restricting - number of filtered test examples: 500\n"
     ]
    }
   ],
   "source": [
    "x_train, y_train = filter_35(x_train, y_train)\n",
    "x_test, y_test = filter_35(x_test, y_test)\n",
    "\n",
    "print(\"Number of filtered training examples:\", len(x_train))\n",
    "print(\"Number of filtered test examples:\", len(x_test))\n",
    "\n",
    "def build_set(x, y, desired_size, t_rate):\n",
    "    assert len(x) == len(y)\n",
    "    r = list(range(len(x)))\n",
    "    np.random.shuffle(r)\n",
    "    \n",
    "    if desired_size is None or t_rate is None:\n",
    "        return x,y # no change\n",
    "    \n",
    "    n_true_max = int(desired_size * t_rate)\n",
    "    n_false_max = desired_size - n_true_max\n",
    "    \n",
    "    n_true = 0\n",
    "    n_false = 0\n",
    "    \n",
    "    res_x = []\n",
    "    res_y = []\n",
    "    \n",
    "    for i in r:\n",
    "        if y[i] == True and n_true < n_true_max:\n",
    "            res_x.append(x[i])\n",
    "            res_y.append(y[i])\n",
    "            n_true += 1\n",
    "        elif y[i] == False and n_false < n_false_max:\n",
    "            res_x.append(x[i])\n",
    "            res_y.append(y[i])\n",
    "            n_false += 1\n",
    "    \n",
    "    assert len(res_x) == len(res_y) and len(res_x) == desired_size\n",
    "    \n",
    "    return np.array(res_x), np.array(res_y)\n",
    "\n",
    "# We do a lot of computation so we want to limit the number of examples ASAP\n",
    "x_train, y_train = build_set(x_train, y_train, NUM_EXAMPLES, 0.3)\n",
    "x_test, y_test = build_set(x_test, y_test, NUM_EXAMPLES, 0.7)\n",
    "\n",
    "\n",
    "print(np.count_nonzero(y_train) / NUM_EXAMPLES)\n",
    "print(np.count_nonzero(y_test) / NUM_EXAMPLES)\n",
    "\n",
    "\n",
    "print(\"After restricting - number of filtered training examples:\", len(x_train))\n",
    "print(\"After restricting - number of filtered test examples:\", len(x_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of x_train is (500, 28, 28, 1)\n",
      "type of x_train is <class 'numpy.ndarray'>\n",
      "shape of x_test is (500, 28, 28, 1)\n",
      "type of x_test is <class 'numpy.ndarray'>\n",
      "shape of x_train_deskew is (500, 28, 28, 1)\n",
      "type of x_train_deskew is <class 'numpy.ndarray'>\n",
      "shape of x_test_deskew is (500, 28, 28, 1)\n",
      "type of x_test_deskew is <class 'numpy.ndarray'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-5-33d05ce432eb>:69: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  plt.subplot(1, 2, 1)\n",
      "<ipython-input-5-33d05ce432eb>:73: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  plt.subplot(1, 2, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9708223e50>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The following moment and deskew functions were taken from the works of :\n",
    "\n",
    "# https://stackoverflow.com/questions/43577665/deskew-mnist-images\n",
    "# https://fsix.github.io/mnist/Deskewing.html\n",
    "\n",
    "from scipy.ndimage import interpolation\n",
    "\n",
    "def moments(image):\n",
    "    c0,c1 = np.mgrid[:image.shape[0],:image.shape[1]] # A trick in numPy to create a mesh grid\n",
    "    totalImage = np.sum(image) #sum of pixels\n",
    "    m0 = np.sum(c0*image)/totalImage #mu_x\n",
    "    m1 = np.sum(c1*image)/totalImage #mu_y\n",
    "    m00 = np.sum((c0-m0)**2*image)/totalImage #var(x)\n",
    "    m11 = np.sum((c1-m1)**2*image)/totalImage #var(y)\n",
    "    m01 = np.sum((c0-m0)*(c1-m1)*image)/totalImage #covariance(x,y)\n",
    "    mu_vector = np.array([m0,m1]) # Notice that these are \\mu_x, \\mu_y respectively\n",
    "    covariance_matrix = np.array([[m00,m01],[m01,m11]]) # Do you see a similarity between the covariance matrix\n",
    "    return mu_vector, covariance_matrix\n",
    "#Deskew the training samples \n",
    "def deskew(image):\n",
    "    c,v = moments(image)\n",
    "    alpha = v[0,1]/v[0,0]\n",
    "    affine = np.array([[1,0],[alpha,1]])\n",
    "    ocenter = np.array(image.shape)/2.0\n",
    "    offset = c-np.dot(affine,ocenter)\n",
    "    img = interpolation.affine_transform(image,affine,offset=offset)\n",
    "    return (img - img.min()) / (img.max() - img.min())\n",
    "\n",
    "print(\"shape of x_train is \" + str(x_train.shape))\n",
    "print(\"type of x_train is \" + str(type(x_train)))\n",
    "print(\"shape of x_test is \" + str(x_test.shape))\n",
    "print(\"type of x_test is \" + str(type(x_test)))\n",
    "\n",
    "\n",
    "#store the deskwed x_train into a list x_train_deskew\n",
    "#store the deskwed x_test into a list x_test_deskew\n",
    "\n",
    "#training set \n",
    "x_train_deskew = [] \n",
    "for i in range(x_train.shape[0]): \n",
    "    x_train_deskew.append(deskew(x_train[i].reshape(28,28)))\n",
    "x_train_deskew = np.array(x_train_deskew)\n",
    "x_train_deskew = x_train_deskew[..., np.newaxis]\n",
    "print(\"shape of x_train_deskew is \" + str(np.shape(x_train_deskew)))\n",
    "print(\"type of x_train_deskew is \" + str(type(x_train_deskew)))\n",
    "\n",
    "#test set \n",
    "x_test_deskew = [] \n",
    "for j in range(x_test.shape[0]): \n",
    "    x_test_deskew.append(deskew(x_test[j].reshape(28,28)))\n",
    "x_test_deskew = np.array(x_test_deskew)\n",
    "x_test_deskew = x_test_deskew[..., np.newaxis]\n",
    "print(\"shape of x_test_deskew is \" + str(np.shape(x_test_deskew)))\n",
    "print(\"type of x_test_deskew is \" + str(type(x_test_deskew)))\n",
    "\n",
    "\n",
    "#We should have the deskewed image stored within x_train\n",
    "#original \n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(x_train[3].reshape(28,28))\n",
    "\n",
    "#deskewed \n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(x_train_deskew[3])\n",
    "\n",
    "\n",
    "#We should have the deskewed image stored within x_test \n",
    "#original\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(x_test[3].reshape(28,28))\n",
    "\n",
    "#deskewed\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(x_test_deskew[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3wyiaP0Xojg_"
   },
   "source": [
    "Show the first example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "j5STP7MbojhA",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f96e6b61be0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(y_train[0])\n",
    "\n",
    "plt.imshow(x_train[0, :, :, 0])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wNS9sVPQojhC"
   },
   "source": [
    "### 1.2 Downscale the images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fmmtplIFGL6t"
   },
   "source": [
    "An image size of 28x28 is much too large for current quantum computers. Resize the image down to 16x16:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lbhUdBFWojhE",
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 16x16 for amplitude embedding!\n",
    "x_train_small_256 = tf.image.resize(x_train, (16,16)).numpy()\n",
    "x_test_small_256 = tf.image.resize(x_test, (16,16)).numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pOMd7zIjGL6x"
   },
   "source": [
    "Again, display the first training example—after resize: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f96e6f20160>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(y_train[0])\n",
    "\n",
    "plt.imshow(x_train_small_256[0,:,:,0], vmin=0, vmax=1)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SlJ5NVaPojhT"
   },
   "source": [
    "### 1.4 Encode the data as quantum circuits\n",
    "\n",
    "To process images using a quantum computer, <a href=\"https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.032308\" class=\"external\">Schuld et al.</a> proposed using amplitude encoding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oLyxS9KlojhZ"
   },
   "source": [
    "We apply ampltidue encoding using the Mottonen state preparation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# tolerance for normalization\n",
    "TOLERANCE = 1e-10\n",
    "\n",
    "# Use Mottonen state preparation to get an amplitude embedding of the states\n",
    "# Adapted from https://pennylane.readthedocs.io/en/stable/_modules/pennylane/templates/state_preparations/mottonen.html#MottonenStatePreparation\n",
    "\n",
    "def gray_code(rank):\n",
    "    \"\"\"Generates the Gray code of given rank.\n",
    "\n",
    "    Args:\n",
    "        rank (int): rank of the Gray code (i.e. number of bits)\n",
    "    \"\"\"\n",
    "\n",
    "    def gray_code_recurse(g, rank):\n",
    "        k = len(g)\n",
    "        if rank <= 0:\n",
    "            return\n",
    "\n",
    "        for i in range(k - 1, -1, -1):\n",
    "            char = \"1\" + g[i]\n",
    "            g.append(char)\n",
    "        for i in range(k - 1, -1, -1):\n",
    "            g[i] = \"0\" + g[i]\n",
    "\n",
    "        gray_code_recurse(g, rank - 1)\n",
    "\n",
    "    g = [\"0\", \"1\"]\n",
    "    gray_code_recurse(g, rank - 1)\n",
    "\n",
    "    return g\n",
    "\n",
    "\n",
    "def _matrix_M_entry(row, col):\n",
    "    \"\"\"Returns one entry for the matrix that maps alpha to theta.\n",
    "\n",
    "    See Eq. (3) in `Möttönen et al. (2004) <https://arxiv.org/pdf/quant-ph/0407010.pdf>`_.\n",
    "\n",
    "    Args:\n",
    "        row (int): one-based row number\n",
    "        col (int): one-based column number\n",
    "\n",
    "    Returns:\n",
    "        (float): transformation matrix entry at given row and column\n",
    "    \"\"\"\n",
    "    # (col >> 1) ^ col is the Gray code of col\n",
    "    b_and_g = row & ((col >> 1) ^ col)\n",
    "    sum_of_ones = 0\n",
    "    while b_and_g > 0:\n",
    "        if b_and_g & 0b1:\n",
    "            sum_of_ones += 1\n",
    "\n",
    "        b_and_g = b_and_g >> 1\n",
    "\n",
    "    return (-1) ** sum_of_ones\n",
    "\n",
    "\n",
    "def _compute_theta(alpha):\n",
    "    \"\"\"Maps the angles alpha of the multi-controlled rotations decomposition of a uniformly controlled rotation\n",
    "     to the rotation angles used in the Gray code implementation.\n",
    "\n",
    "    Args:\n",
    "        alpha (tensor_like): alpha parameters\n",
    "\n",
    "    Returns:\n",
    "        (tensor_like): rotation angles theta\n",
    "    \"\"\"\n",
    "    ln = alpha.shape[0]\n",
    "    k = np.log2(alpha.shape[0])\n",
    "\n",
    "    M_trans = np.zeros(shape=(ln, ln))\n",
    "    for i in range(len(M_trans)):\n",
    "        for j in range(len(M_trans[0])):\n",
    "            M_trans[i, j] = _matrix_M_entry(j, i)\n",
    "\n",
    "    theta = np.dot(M_trans, alpha)\n",
    "\n",
    "    return theta / 2 ** k\n",
    "\n",
    "\n",
    "def _uniform_rotation_dagger(gate, alpha, control_wires, target_wire, circuit):\n",
    "    r\"\"\"Applies a uniformly-controlled rotation to the target qubit.\n",
    "\n",
    "    A uniformly-controlled rotation is a sequence of multi-controlled\n",
    "    rotations, each of which is conditioned on the control qubits being in a different state.\n",
    "    For example, a uniformly-controlled rotation with two control qubits describes a sequence of\n",
    "    four multi-controlled rotations, each applying the rotation only if the control qubits\n",
    "    are in states :math:`|00\\rangle`, :math:`|01\\rangle`, :math:`|10\\rangle`, and :math:`|11\\rangle`, respectively.\n",
    "\n",
    "    To implement a uniformly-controlled rotation using single qubit rotations and CNOT gates,\n",
    "    a decomposition based on Gray codes is used. For this purpose, the multi-controlled rotation\n",
    "    angles alpha have to be converted into a set of non-controlled rotation angles theta.\n",
    "\n",
    "    For more details, see `Möttönen and Vartiainen (2005), Fig 7a<https://arxiv.org/pdf/quant-ph/0504100.pdf>`_.\n",
    "\n",
    "    Args:\n",
    "        gate (.Operation): gate to be applied, needs to have exactly one parameter\n",
    "        alpha (tensor_like): angles to decompose the uniformly-controlled rotation into multi-controlled rotations\n",
    "        control_wires (array[int]): wires that act as control\n",
    "        target_wire (int): wire that acts as target\n",
    "    \"\"\"\n",
    "\n",
    "    theta = _compute_theta(alpha)\n",
    "\n",
    "    gray_code_rank = len(control_wires)\n",
    "\n",
    "    if gray_code_rank == 0:\n",
    "        if theta[0] != 0.0:\n",
    "            circuit.append(gate(theta[0])(target_wire))\n",
    "        return\n",
    "\n",
    "    code = gray_code(gray_code_rank)\n",
    "    num_selections = len(code)\n",
    "\n",
    "    control_indices = [\n",
    "        int(np.log2(int(code[i], 2) ^ int(code[(i + 1) % num_selections], 2)))\n",
    "        for i in range(num_selections)\n",
    "    ]\n",
    "\n",
    "    for i, control_index in enumerate(control_indices):\n",
    "        if theta[i] != 0.0:\n",
    "            circuit.append(gate(theta[i])(target_wire))\n",
    "        circuit.append(cirq.CNOT(control_wires[control_index], target_wire))\n",
    "\n",
    "\n",
    "def _get_alpha_z(omega, n, k):\n",
    "    r\"\"\"Computes the rotation angles required to implement the uniformly-controlled Z rotation\n",
    "    applied to the :math:`k`th qubit.\n",
    "\n",
    "    The :math:`j`th angle is related to the phases omega of the desired amplitudes via:\n",
    "\n",
    "    .. math:: \\alpha^{z,k}_j = \\sum_{l=1}^{2^{k-1}} \\frac{\\omega_{(2j-1) 2^{k-1}+l} - \\omega_{(2j-2) 2^{k-1}+l}}{2^{k-1}}\n",
    "\n",
    "    Args:\n",
    "        omega (tensor_like): phases of the state to prepare\n",
    "        n (int): total number of qubits for the uniformly-controlled rotation\n",
    "        k (int): index of current qubit\n",
    "\n",
    "    Returns:\n",
    "        array representing :math:`\\alpha^{z,k}`\n",
    "    \"\"\"\n",
    "    indices1 = [\n",
    "        [(2 * j - 1) * 2 ** (k - 1) + l - 1 for l in range(1, 2 ** (k - 1) + 1)]\n",
    "        for j in range(1, 2 ** (n - k) + 1)\n",
    "    ]\n",
    "    indices2 = [\n",
    "        [(2 * j - 2) * 2 ** (k - 1) + l - 1 for l in range(1, 2 ** (k - 1) + 1)]\n",
    "        for j in range(1, 2 ** (n - k) + 1)\n",
    "    ]\n",
    "\n",
    "    term1 = np.take(omega, indices=indices1)\n",
    "    term2 = np.take(omega, indices=indices2)\n",
    "    diff = (term1 - term2) / 2 ** (k - 1)\n",
    "\n",
    "    return np.sum(diff, axis=1)\n",
    "\n",
    "\n",
    "def _get_alpha_y(a, n, k):\n",
    "    r\"\"\"Computes the rotation angles required to implement the uniformly controlled Y rotation\n",
    "    applied to the :math:`k`th qubit.\n",
    "\n",
    "    The :math:`j`-th angle is related to the absolute values, a, of the desired amplitudes via:\n",
    "\n",
    "    .. math:: \\alpha^{y,k}_j = 2 \\arcsin \\sqrt{ \\frac{ \\sum_{l=1}^{2^{k-1}} a_{(2j-1)2^{k-1} +l}^2  }{ \\sum_{l=1}^{2^{k}} a_{(j-1)2^{k} +l}^2  } }\n",
    "\n",
    "    Args:\n",
    "        a (tensor_like): absolute values of the state to prepare\n",
    "        n (int): total number of qubits for the uniformly-controlled rotation\n",
    "        k (int): index of current qubit\n",
    "\n",
    "    Returns:\n",
    "        array representing :math:`\\alpha^{y,k}`\n",
    "    \"\"\"\n",
    "    indices_numerator = [\n",
    "        [(2 * (j + 1) - 1) * 2 ** (k - 1) + l for l in range(2 ** (k - 1))]\n",
    "        for j in range(2 ** (n - k))\n",
    "    ]\n",
    "    numerator = np.take(a, indices=indices_numerator)\n",
    "    numerator = np.sum(np.abs(numerator) ** 2, axis=1)\n",
    "\n",
    "    indices_denominator = [[j * 2 ** k + l for l in range(2 ** k)] for j in range(2 ** (n - k))]\n",
    "    denominator = np.take(a, indices=indices_denominator)\n",
    "    denominator = np.sum(np.abs(denominator) ** 2, axis=1)\n",
    "\n",
    "    # Divide only where denominator is zero, else leave initial value of zero.\n",
    "    # The equation guarantees that the numerator is also zero in the corresponding entries.\n",
    "\n",
    "    with np.errstate(divide=\"ignore\", invalid=\"ignore\"):\n",
    "        division = numerator / denominator\n",
    "\n",
    "    division = np.where(denominator != 0.0, division, 0.0)\n",
    "\n",
    "    return 2 * np.arcsin(np.sqrt(division))\n",
    "\n",
    "def mottonenStatePrep(state_vector, qubits, circuit):\n",
    "\n",
    "        a = np.abs(state_vector)\n",
    "        omega = np.angle(state_vector)\n",
    "\n",
    "        # change ordering of wires, since original code\n",
    "        # was written for IBM machines\n",
    "        wires_reverse = qubits[::-1]\n",
    "\n",
    "        # Apply inverse y rotation cascade to prepare correct absolute values of amplitudes\n",
    "        for k in range(len(wires_reverse), 0, -1):\n",
    "            alpha_y_k = _get_alpha_y(a, len(wires_reverse), k)\n",
    "            control = wires_reverse[k:]\n",
    "            target = wires_reverse[k - 1]\n",
    "            _uniform_rotation_dagger(cirq.ry, alpha_y_k, control, target, circuit)\n",
    "\n",
    "        # If necessary, apply inverse z rotation cascade to prepare correct phases of amplitudes\n",
    "        if not np.allclose(omega, 0):\n",
    "            for k in range(len(wires_reverse), 0, -1):\n",
    "                alpha_z_k = _get_alpha_z(omega, len(wires_reverse), k)\n",
    "                control = wires_reverse[k:]\n",
    "                target = wires_reverse[k - 1]\n",
    "                if len(alpha_z_k) > 0:\n",
    "                    _uniform_rotation_dagger(cirq.rz, alpha_z_k, control, target, circuit)\n",
    "\n",
    "         \n",
    "# The below is borrowed from https://pennylane.readthedocs.io/en/stable/_modules/pennylane/templates/embeddings/amplitude.html#AmplitudeEmbedding\n",
    "def _preprocess(features, wires, pad_with, normalize):\n",
    "    \"\"\"Validate and pre-process inputs as follows:\n",
    "\n",
    "    * Check that the features tensor is one-dimensional.\n",
    "    * If pad_with is None, check that the first dimension of the features tensor\n",
    "      has length :math:`2^n` where :math:`n` is the number of qubits. Else check that the\n",
    "      first dimension of the features tensor is not larger than :math:`2^n` and pad features with value if necessary.\n",
    "    * If normalize is false, check that first dimension of features is normalised to one. Else, normalise the\n",
    "      features tensor.\n",
    "    \"\"\"\n",
    "\n",
    "    shape = features.shape\n",
    "\n",
    "    # check shape\n",
    "    if features.ndim != 1:\n",
    "        raise ValueError(f\"Features must be a one-dimensional tensor; got shape {shape}.\")\n",
    "\n",
    "    n_features = shape[0]\n",
    "    if pad_with is None and n_features != 2 ** len(wires):\n",
    "        raise ValueError(\n",
    "            f\"Features must be of length {2 ** len(wires)}; got length {n_features}. \"\n",
    "            f\"Use the 'pad' argument for automated padding.\"\n",
    "        )\n",
    "\n",
    "    if pad_with is not None and n_features > 2 ** len(wires):\n",
    "        raise ValueError(\n",
    "            f\"Features must be of length {2 ** len(wires)} or \"\n",
    "            f\"smaller to be padded; got length {n_features}.\"\n",
    "        )\n",
    "\n",
    "    # pad\n",
    "    if pad_with is not None and n_features < 2 ** len(wires):\n",
    "        padding = [pad_with] * (2 ** len(wires) - n_features)\n",
    "        features = np.concatenate([features, padding], axis=0)\n",
    "\n",
    "    # normalize\n",
    "    norm = np.sum(np.abs(features) ** 2)\n",
    "\n",
    "    if not np.allclose(norm, 1.0, atol=TOLERANCE):\n",
    "        if normalize or pad_with:\n",
    "            features = features / np.sqrt(norm)\n",
    "        else:\n",
    "            raise ValueError(\n",
    "                f\"Features must be a vector of length 1.0; got length {norm}.\"\n",
    "                \"Use 'normalize=True' to automatically normalize.\"\n",
    "            )\n",
    "\n",
    "    features = features.astype(np.complex128)\n",
    "    return features\n",
    "\n",
    "def cirqAppendAmplitudeEmbedding(features, qubits, circuit, pad_with=None, normalize=False):\n",
    "    features = _preprocess(features, qubits, pad_with, normalize)\n",
    "    mottonenStatePrep(features, qubits, circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aOu_3-3ZGL61",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def convert_to_circuit(image):\n",
    "    \"\"\"Encode truncated classical image into quantum datapoint.\"\"\"\n",
    "    values = np.ndarray.flatten(image)\n",
    "    qubits = cirq.GridQubit.rect(4, 4)\n",
    "    circuit = cirq.Circuit()\n",
    "    for i, value in enumerate(values):\n",
    "        if value:\n",
    "            circuit.append(cirq.X(qubits[i]))\n",
    "    circuit.append(make_qft(qubits))\n",
    "    return circuit\n",
    "\n",
    "def convert_to_circuit_mottonen(image):\n",
    "    values = np.ndarray.flatten(image)\n",
    "    assert len(values) == 256\n",
    "    qubits = cirq.GridQubit.rect(4, 2)\n",
    "    circuit = cirq.Circuit()\n",
    "    cirqAppendAmplitudeEmbedding(values, qubits, circuit, normalize=True)\n",
    "    return circuit\n",
    "\n",
    "#x_train_circ = [convert_to_circuit(x) for x in x_train_bin]\n",
    "#x_test_circ = [convert_to_circuit(x) for x in x_test_bin]\n",
    "\n",
    "x_train_circ = [convert_to_circuit_mottonen(x) for x in x_train_small_256]\n",
    "x_test_circ = [convert_to_circuit_mottonen(x) for x in x_test_small_256]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zSCXqzOzojhd"
   },
   "source": [
    "Here is the circuit created for the first example (circuit diagrams do not show qubits with zero gates):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "w3POmUEUojhe",
    "tags": []
   },
   "outputs": [
    {
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x2=\"36623.174296875106\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"36787.35816406261\" x2=\"36787.35816406261\" y1=\"275.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"36946.87992187511\" x2=\"36946.87992187511\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"37106.40167968761\" x2=\"37106.40167968761\" y1=\"225.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"37270.58554687511\" x2=\"37270.58554687511\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"37430.10730468761\" x2=\"37430.10730468761\" y1=\"275.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"37552.72183593761\" x2=\"37552.72183593761\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"37716.905703125114\" x2=\"37716.905703125114\" y1=\"125.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"37876.427460937615\" x2=\"37876.427460937615\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38035.94921875012\" x2=\"38035.94921875012\" y1=\"275.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38195.47097656262\" x2=\"38195.47097656262\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38359.65484375012\" x2=\"38359.65484375012\" y1=\"225.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38523.83871093762\" x2=\"38523.83871093762\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38675.57433593762\" x2=\"38675.57433593762\" y1=\"275.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38835.09609375012\" x2=\"38835.09609375012\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"38999.27996093762\" x2=\"38999.27996093762\" y1=\"175.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"39163.463828125125\" x2=\"39163.463828125125\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"39322.985585937626\" x2=\"39322.985585937626\" y1=\"275.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"39482.50734375013\" x2=\"39482.50734375013\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"39646.69121093763\" x2=\"39646.69121093763\" y1=\"225.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"39810.87507812513\" x2=\"39810.87507812513\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"39970.39683593763\" x2=\"39970.39683593763\" y1=\"275.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"40129.91859375013\" x2=\"40129.91859375013\" y1=\"325.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"40289.44035156263\" x2=\"40289.44035156263\" y1=\"25.0\" y2=\"375.0\" stroke=\"black\" stroke-width=\"3\" /><rect x=\"10.0\" y=\"5.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(0, 0): </text><rect x=\"10.0\" y=\"55.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(0, 1): </text><rect x=\"10.0\" y=\"105.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(1, 0): </text><rect x=\"10.0\" y=\"155.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(1, 1): </text><rect x=\"10.0\" y=\"205.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(2, 0): </text><rect x=\"10.0\" y=\"255.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(2, 1): </text><rect x=\"10.0\" y=\"305.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(3, 0): </text><rect x=\"10.0\" y=\"355.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(3, 1): </text><rect x=\"74.49359375\" y=\"5.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.534π)</text><rect x=\"74.49359375\" y=\"55.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.617π)</text><rect x=\"74.49359375\" y=\"105.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.2π)</text><rect x=\"74.49359375\" y=\"155.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.311π)</text><rect x=\"74.49359375\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.189π)</text><rect x=\"74.49359375\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.31π)</text><rect x=\"74.49359375\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.186π)</text><rect x=\"74.49359375\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.134π)</text><circle cx=\"194.0153515625\" cy=\"25.0\" r=\"10.0\" /><rect x=\"174.0153515625\" y=\"55.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"194.0153515625\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"234.01535156249997\" y=\"55.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"273.77623046875\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.383π)</text><circle cx=\"353.537109375\" cy=\"25.0\" r=\"10.0\" /><rect x=\"333.537109375\" y=\"55.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"353.537109375\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><circle cx=\"413.537109375\" cy=\"75.0\" r=\"10.0\" /><rect x=\"393.537109375\" y=\"105.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"413.537109375\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"453.537109375\" y=\"105.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"493.29798828125\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.054π)</text><circle cx=\"573.0588671875\" cy=\"25.0\" r=\"10.0\" /><rect x=\"553.0588671875\" y=\"105.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"573.0588671875\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"613.0588671875\" y=\"105.0\" width=\"68.6116015625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"647.36466796875\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.2π)</text><circle cx=\"721.67046875\" cy=\"75.0\" r=\"10.0\" /><rect x=\"701.67046875\" y=\"105.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"721.67046875\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"761.67046875\" y=\"105.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"803.7624023437501\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.054π)</text><circle cx=\"885.8543359375001\" cy=\"25.0\" r=\"10.0\" /><rect x=\"865.8543359375001\" y=\"105.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"885.8543359375001\" y=\"125.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><circle cx=\"945.8543359375001\" cy=\"125.0\" r=\"10.0\" /><rect x=\"925.8543359375001\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"945.8543359375001\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"985.8543359375\" y=\"155.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1025.61521484375\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.021π)</text><circle cx=\"1105.37609375\" cy=\"75.0\" r=\"10.0\" /><rect x=\"1085.37609375\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1105.37609375\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"1145.37609375\" y=\"155.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1187.46802734375\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.017π)</text><circle cx=\"1269.5599609375001\" cy=\"125.0\" r=\"10.0\" /><rect x=\"1249.5599609375001\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1269.5599609375001\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"1309.5599609375001\" y=\"155.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1351.65189453125\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.033π)</text><circle cx=\"1433.7438281250002\" cy=\"25.0\" r=\"10.0\" /><rect x=\"1413.7438281250002\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1433.7438281250002\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"1473.7438281250002\" y=\"155.0\" width=\"83.1513671875\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1515.3195117187502\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.311π)</text><circle cx=\"1596.8951953125002\" cy=\"125.0\" r=\"10.0\" /><rect x=\"1576.8951953125002\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1596.8951953125002\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"1636.8951953125002\" y=\"155.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1678.98712890625\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.021π)</text><circle cx=\"1761.0790625000002\" cy=\"75.0\" r=\"10.0\" /><rect x=\"1741.0790625000002\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1761.0790625000002\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"1801.0790625000002\" y=\"155.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1840.83994140625\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.017π)</text><circle cx=\"1920.6008203125002\" cy=\"125.0\" r=\"10.0\" /><rect x=\"1900.6008203125002\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1920.6008203125002\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"1960.6008203125002\" y=\"155.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2000.3616992187501\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.033π)</text><circle cx=\"2080.122578125\" cy=\"25.0\" r=\"10.0\" /><rect x=\"2060.122578125\" y=\"155.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2080.122578125\" y=\"175.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><circle cx=\"2140.122578125\" cy=\"175.0\" r=\"10.0\" /><rect x=\"2120.122578125\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2140.122578125\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"2180.122578125\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2219.88345703125\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.022π)</text><circle cx=\"2299.6443359375\" cy=\"125.0\" r=\"10.0\" /><rect x=\"2279.6443359375\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2299.6443359375\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"2339.6443359375\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2381.73626953125\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.054π)</text><circle cx=\"2463.8282031249996\" cy=\"175.0\" r=\"10.0\" /><rect x=\"2443.8282031249996\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2463.8282031249996\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"2503.8282031249996\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2543.5890820312497\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.097π)</text><circle cx=\"2623.3499609374994\" cy=\"75.0\" r=\"10.0\" /><rect x=\"2603.3499609374994\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2623.3499609374994\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"2663.3499609374994\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2705.4418945312495\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.121π)</text><circle cx=\"2787.533828124999\" cy=\"175.0\" r=\"10.0\" /><rect x=\"2767.533828124999\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2787.533828124999\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"2827.533828124999\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2869.6257617187493\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.025π)</text><circle cx=\"2951.717695312499\" cy=\"125.0\" r=\"10.0\" /><rect x=\"2931.717695312499\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"2951.717695312499\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"2991.717695312499\" y=\"205.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3029.916562499999\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.01π)</text><circle cx=\"3108.115429687499\" cy=\"175.0\" r=\"10.0\" /><rect x=\"3088.115429687499\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3108.115429687499\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"3148.115429687499\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3190.207363281249\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.089π)</text><circle cx=\"3272.2992968749986\" cy=\"25.0\" r=\"10.0\" /><rect x=\"3252.2992968749986\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3272.2992968749986\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"3312.2992968749986\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3354.3912304687487\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.189π)</text><circle cx=\"3436.4831640624984\" cy=\"175.0\" r=\"10.0\" /><rect x=\"3416.4831640624984\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3436.4831640624984\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"3476.4831640624984\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3518.5750976562485\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.022π)</text><circle cx=\"3600.667031249998\" cy=\"125.0\" r=\"10.0\" /><rect x=\"3580.667031249998\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3600.667031249998\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"3640.667031249998\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3680.4279101562483\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.054π)</text><circle cx=\"3760.188789062498\" cy=\"175.0\" r=\"10.0\" /><rect x=\"3740.188789062498\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3760.188789062498\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"3800.188789062498\" y=\"205.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3842.280722656248\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.097π)</text><circle cx=\"3924.372656249998\" cy=\"75.0\" r=\"10.0\" /><rect x=\"3904.372656249998\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"3924.372656249998\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"3964.372656249998\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4004.133535156248\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.121π)</text><circle cx=\"4083.8944140624976\" cy=\"175.0\" r=\"10.0\" /><rect x=\"4063.8944140624976\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4083.8944140624976\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"4123.894414062497\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4163.655292968747\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.025π)</text><circle cx=\"4243.416171874997\" cy=\"125.0\" r=\"10.0\" /><rect x=\"4223.416171874997\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4243.416171874997\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"4283.416171874997\" y=\"205.0\" width=\"71.735625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4319.283984374997\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.01π)</text><circle cx=\"4395.151796874998\" cy=\"175.0\" r=\"10.0\" /><rect x=\"4375.151796874998\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4395.151796874998\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"4435.151796874998\" y=\"205.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4474.912675781247\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.089π)</text><circle cx=\"4554.673554687498\" cy=\"25.0\" r=\"10.0\" /><rect x=\"4534.673554687498\" y=\"205.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4554.673554687498\" y=\"225.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><circle cx=\"4614.673554687498\" cy=\"225.0\" r=\"10.0\" /><rect x=\"4594.673554687498\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4614.673554687498\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"4654.673554687498\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4694.434433593748\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.235π)</text><circle cx=\"4774.195312499998\" cy=\"175.0\" r=\"10.0\" /><rect x=\"4754.195312499998\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4774.195312499998\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"4814.195312499998\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4853.956191406248\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.016π)</text><circle cx=\"4933.717070312498\" cy=\"225.0\" r=\"10.0\" /><rect x=\"4913.717070312498\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"4933.717070312498\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"4973.717070312498\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5013.477949218748\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.046π)</text><circle cx=\"5093.238828124999\" cy=\"125.0\" r=\"10.0\" /><rect x=\"5073.238828124999\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5093.238828124999\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"5133.238828124999\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5172.999707031248\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.041π)</text><circle cx=\"5252.760585937499\" cy=\"225.0\" r=\"10.0\" /><rect x=\"5232.760585937499\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5252.760585937499\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"5292.760585937499\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5332.521464843749\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.013π)</text><circle cx=\"5412.282343749999\" cy=\"175.0\" r=\"10.0\" /><rect x=\"5392.282343749999\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5412.282343749999\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"5452.282343749999\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5494.374277343749\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.001π)</text><circle cx=\"5576.466210937499\" cy=\"225.0\" r=\"10.0\" /><rect x=\"5556.466210937499\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5576.466210937499\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"5616.466210937499\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5656.227089843749\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.072π)</text><circle cx=\"5735.98796875\" cy=\"75.0\" r=\"10.0\" /><rect x=\"5715.98796875\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5735.98796875\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"5775.98796875\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5818.079902343749\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.059π)</text><circle cx=\"5900.1718359375\" cy=\"225.0\" r=\"10.0\" /><rect x=\"5880.1718359375\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5900.1718359375\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"5940.1718359375\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"5979.93271484375\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.014π)</text><circle cx=\"6059.69359375\" cy=\"175.0\" r=\"10.0\" /><rect x=\"6039.69359375\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6059.69359375\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"6099.69359375\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6141.78552734375\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.017π)</text><circle cx=\"6223.8774609375005\" cy=\"225.0\" r=\"10.0\" /><rect x=\"6203.8774609375005\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6223.8774609375005\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"6263.8774609375005\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6305.96939453125\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.045π)</text><circle cx=\"6388.061328125001\" cy=\"125.0\" r=\"10.0\" /><rect x=\"6368.061328125001\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6388.061328125001\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"6428.061328125001\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6470.15326171875\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.042π)</text><circle cx=\"6552.245195312501\" cy=\"225.0\" r=\"10.0\" /><rect x=\"6532.245195312501\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6552.245195312501\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"6592.245195312501\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6634.337128906251\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.012π)</text><circle cx=\"6716.429062500001\" cy=\"175.0\" r=\"10.0\" /><rect x=\"6696.429062500001\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6716.429062500001\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"6756.429062500001\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6796.189941406251\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.002π)</text><circle cx=\"6875.9508203125015\" cy=\"225.0\" r=\"10.0\" /><rect x=\"6855.9508203125015\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6875.9508203125015\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"6915.9508203125015\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"6958.042753906251\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.073π)</text><circle cx=\"7040.134687500002\" cy=\"25.0\" r=\"10.0\" /><rect x=\"7020.134687500002\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7040.134687500002\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"7080.134687500002\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7122.226621093751\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.252π)</text><circle cx=\"7204.318554687502\" cy=\"225.0\" r=\"10.0\" /><rect x=\"7184.318554687502\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7204.318554687502\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"7244.318554687502\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7286.410488281252\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.177π)</text><circle cx=\"7368.502421875002\" cy=\"175.0\" r=\"10.0\" /><rect x=\"7348.502421875002\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7368.502421875002\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"7408.502421875002\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7448.263300781252\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.042π)</text><circle cx=\"7528.0241796875025\" cy=\"225.0\" r=\"10.0\" /><rect x=\"7508.0241796875025\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7528.0241796875025\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"7568.0241796875025\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7607.785058593752\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.012π)</text><circle cx=\"7687.545937500003\" cy=\"125.0\" r=\"10.0\" /><rect x=\"7667.545937500003\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7687.545937500003\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"7727.545937500003\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7767.306816406252\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.017π)</text><circle cx=\"7847.067695312503\" cy=\"225.0\" r=\"10.0\" /><rect x=\"7827.067695312503\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7847.067695312503\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"7887.067695312503\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"7926.828574218753\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.045π)</text><circle cx=\"8006.589453125003\" cy=\"175.0\" r=\"10.0\" /><rect x=\"7986.589453125003\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8006.589453125003\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"8046.589453125003\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8086.350332031253\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.059π)</text><circle cx=\"8166.1112109375035\" cy=\"225.0\" r=\"10.0\" /><rect x=\"8146.1112109375035\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8166.1112109375035\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"8206.111210937503\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8248.203144531253\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.014π)</text><circle cx=\"8330.295078125002\" cy=\"75.0\" r=\"10.0\" /><rect x=\"8310.295078125002\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8330.295078125002\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"8370.295078125002\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8410.055957031253\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.001π)</text><circle cx=\"8489.816835937501\" cy=\"225.0\" r=\"10.0\" /><rect x=\"8469.816835937501\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8489.816835937501\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"8529.816835937501\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8571.908769531252\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.072π)</text><circle cx=\"8654.000703125\" cy=\"175.0\" r=\"10.0\" /><rect x=\"8634.000703125\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8654.000703125\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"8694.000703125\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8736.092636718751\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.041π)</text><circle cx=\"8818.1845703125\" cy=\"225.0\" r=\"10.0\" /><rect x=\"8798.1845703125\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8818.1845703125\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"8858.1845703125\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8900.27650390625\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.013π)</text><circle cx=\"8982.3684375\" cy=\"125.0\" r=\"10.0\" /><rect x=\"8962.3684375\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"8982.3684375\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"9022.3684375\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9064.46037109375\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.016π)</text><circle cx=\"9146.552304687499\" cy=\"225.0\" r=\"10.0\" /><rect x=\"9126.552304687499\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9146.552304687499\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"9186.552304687499\" y=\"255.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9228.64423828125\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.046π)</text><circle cx=\"9310.736171874998\" cy=\"175.0\" r=\"10.0\" /><rect x=\"9290.736171874998\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9310.736171874998\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"9350.736171874998\" y=\"255.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9388.935039062499\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.06π)</text><circle cx=\"9467.133906249997\" cy=\"225.0\" r=\"10.0\" /><rect x=\"9447.133906249997\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9467.133906249997\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"9507.133906249997\" y=\"255.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9546.894785156248\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.015π)</text><circle cx=\"9626.655664062497\" cy=\"25.0\" r=\"10.0\" /><rect x=\"9606.655664062497\" y=\"255.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9626.655664062497\" y=\"275.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><circle cx=\"9686.655664062497\" cy=\"275.0\" r=\"10.0\" /><rect x=\"9666.655664062497\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9686.655664062497\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"9726.655664062497\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9768.747597656247\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.038π)</text><circle cx=\"9850.839531249996\" cy=\"225.0\" r=\"10.0\" /><rect x=\"9830.839531249996\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9850.839531249996\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"9890.839531249996\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"9932.931464843747\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.073π)</text><circle cx=\"10015.023398437495\" cy=\"275.0\" r=\"10.0\" /><rect x=\"9995.023398437495\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10015.023398437495\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"10055.023398437495\" y=\"305.0\" width=\"78.4892578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10094.268027343745\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.112π)</text><circle cx=\"10173.512656249995\" cy=\"175.0\" r=\"10.0\" /><rect x=\"10153.512656249995\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10173.512656249995\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"10213.512656249995\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10253.273535156246\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.009π)</text><circle cx=\"10333.034414062495\" cy=\"275.0\" r=\"10.0\" /><rect x=\"10313.034414062495\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10333.034414062495\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"10373.034414062495\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10412.795292968745\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.003π)</text><circle cx=\"10492.556171874994\" cy=\"225.0\" r=\"10.0\" /><rect x=\"10472.556171874994\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10492.556171874994\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"10532.556171874994\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10572.317050781245\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.013π)</text><circle cx=\"10652.077929687493\" cy=\"275.0\" r=\"10.0\" /><rect x=\"10632.077929687493\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10652.077929687493\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"10692.077929687493\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10731.838808593744\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.038π)</text><circle cx=\"10811.599687499993\" cy=\"125.0\" r=\"10.0\" /><rect x=\"10791.599687499993\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10811.599687499993\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"10851.599687499993\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10891.360566406243\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.009π)</text><circle cx=\"10971.121445312492\" cy=\"275.0\" r=\"10.0\" /><rect x=\"10951.121445312492\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"10971.121445312492\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11011.121445312492\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11050.882324218743\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.027π)</text><circle cx=\"11130.643203124991\" cy=\"225.0\" r=\"10.0\" /><rect x=\"11110.643203124991\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11130.643203124991\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11170.643203124991\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11210.404082031242\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.032π)</text><circle cx=\"11290.16496093749\" cy=\"275.0\" r=\"10.0\" /><rect x=\"11270.16496093749\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11290.16496093749\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11330.16496093749\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11372.256894531241\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.006π)</text><circle cx=\"11454.34882812499\" cy=\"175.0\" r=\"10.0\" /><rect x=\"11434.34882812499\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11454.34882812499\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11494.34882812499\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11536.44076171874\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.044π)</text><circle cx=\"11618.53269531249\" cy=\"275.0\" r=\"10.0\" /><rect x=\"11598.53269531249\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11618.53269531249\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11658.53269531249\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11700.62462890624\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.028π)</text><circle cx=\"11782.716562499989\" cy=\"225.0\" r=\"10.0\" /><rect x=\"11762.716562499989\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11782.716562499989\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11822.716562499989\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11864.80849609374\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.007π)</text><circle cx=\"11946.900429687488\" cy=\"275.0\" r=\"10.0\" /><rect x=\"11926.900429687488\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"11946.900429687488\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"11986.900429687488\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12026.661308593739\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.016π)</text><circle cx=\"12106.422187499988\" cy=\"75.0\" r=\"10.0\" /><rect x=\"12086.422187499988\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12106.422187499988\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"12146.422187499988\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12188.514121093738\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.096π)</text><circle cx=\"12270.606054687487\" cy=\"275.0\" r=\"10.0\" /><rect x=\"12250.606054687487\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12270.606054687487\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"12310.606054687487\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12352.697988281237\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.038π)</text><circle cx=\"12434.789921874986\" cy=\"225.0\" r=\"10.0\" /><rect x=\"12414.789921874986\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12434.789921874986\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"12474.789921874986\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12516.881855468737\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.018π)</text><circle cx=\"12598.973789062486\" cy=\"275.0\" r=\"10.0\" /><rect x=\"12578.973789062486\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12598.973789062486\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"12638.973789062486\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12681.065722656236\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.036π)</text><circle cx=\"12763.157656249985\" cy=\"175.0\" r=\"10.0\" /><rect x=\"12743.157656249985\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12763.157656249985\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"12803.157656249985\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12845.249589843736\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.019π)</text><circle cx=\"12927.341523437484\" cy=\"275.0\" r=\"10.0\" /><rect x=\"12907.341523437484\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"12927.341523437484\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"12967.341523437484\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13009.433457031235\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.007π)</text><circle cx=\"13091.525390624984\" cy=\"225.0\" r=\"10.0\" /><rect x=\"13071.525390624984\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13091.525390624984\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"13131.525390624984\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13173.617324218734\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.002π)</text><circle cx=\"13255.709257812483\" cy=\"275.0\" r=\"10.0\" /><rect x=\"13235.709257812483\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13255.709257812483\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"13295.709257812483\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13337.801191406234\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.034π)</text><circle cx=\"13419.893124999982\" cy=\"125.0\" r=\"10.0\" /><rect x=\"13399.893124999982\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13419.893124999982\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"13459.893124999982\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13501.985058593733\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.043π)</text><circle cx=\"13584.076992187482\" cy=\"275.0\" r=\"10.0\" /><rect x=\"13564.076992187482\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13584.076992187482\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"13624.076992187482\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13666.168925781232\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.008π)</text><circle cx=\"13748.260859374981\" cy=\"225.0\" r=\"10.0\" /><rect x=\"13728.260859374981\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13748.260859374981\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"13788.260859374981\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13828.021738281232\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.002π)</text><circle cx=\"13907.78261718748\" cy=\"275.0\" r=\"10.0\" /><rect x=\"13887.78261718748\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13907.78261718748\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"13947.78261718748\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"13989.874550781231\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.013π)</text><circle cx=\"14071.96648437498\" cy=\"175.0\" r=\"10.0\" /><rect x=\"14051.96648437498\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14071.96648437498\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"14111.96648437498\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14151.72736328123\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.034π)</text><circle cx=\"14231.488242187479\" cy=\"275.0\" r=\"10.0\" /><rect x=\"14211.488242187479\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14231.488242187479\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"14271.488242187479\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14311.24912109373\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.052π)</text><circle cx=\"14391.009999999978\" cy=\"225.0\" r=\"10.0\" /><rect x=\"14371.009999999978\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14391.009999999978\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"14431.009999999978\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14470.770878906229\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.017π)</text><circle cx=\"14550.531757812478\" cy=\"275.0\" r=\"10.0\" /><rect x=\"14530.531757812478\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14550.531757812478\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"14590.531757812478\" y=\"305.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14628.730624999978\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.04π)</text><circle cx=\"14706.929492187477\" cy=\"25.0\" r=\"10.0\" /><rect x=\"14686.929492187477\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14706.929492187477\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"14746.929492187477\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14789.021425781228\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.147π)</text><circle cx=\"14871.113359374976\" cy=\"275.0\" r=\"10.0\" /><rect x=\"14851.113359374976\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14871.113359374976\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"14911.113359374976\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"14950.874238281227\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.061π)</text><circle cx=\"15030.635117187476\" cy=\"225.0\" r=\"10.0\" /><rect x=\"15010.635117187476\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15030.635117187476\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"15070.635117187476\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15110.395996093726\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.096π)</text><circle cx=\"15190.156874999975\" cy=\"275.0\" r=\"10.0\" /><rect x=\"15170.156874999975\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15190.156874999975\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"15230.156874999975\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15272.248808593726\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.072π)</text><circle cx=\"15354.340742187474\" cy=\"175.0\" r=\"10.0\" /><rect x=\"15334.340742187474\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15354.340742187474\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"15394.340742187474\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15434.101621093725\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.031π)</text><circle cx=\"15513.862499999974\" cy=\"275.0\" r=\"10.0\" /><rect x=\"15493.862499999974\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15513.862499999974\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"15553.862499999974\" y=\"305.0\" width=\"71.735625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15589.730312499974\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.02π)</text><circle cx=\"15665.598124999973\" cy=\"225.0\" r=\"10.0\" /><rect x=\"15645.598124999973\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15665.598124999973\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"15705.598124999973\" y=\"305.0\" width=\"71.735625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15741.465937499974\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.01π)</text><circle cx=\"15817.333749999972\" cy=\"275.0\" r=\"10.0\" /><rect x=\"15797.333749999972\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15817.333749999972\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"15857.333749999972\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15897.094628906223\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.002π)</text><circle cx=\"15976.855507812472\" cy=\"125.0\" r=\"10.0\" /><rect x=\"15956.855507812472\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"15976.855507812472\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16016.855507812472\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16056.616386718722\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.031π)</text><circle cx=\"16136.377265624971\" cy=\"275.0\" r=\"10.0\" /><rect x=\"16116.377265624971\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16136.377265624971\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16176.377265624971\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16218.469199218722\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.004π)</text><circle cx=\"16300.56113281247\" cy=\"225.0\" r=\"10.0\" /><rect x=\"16280.56113281247\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16300.56113281247\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16340.56113281247\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16382.653066406221\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.009π)</text><circle cx=\"16464.74499999997\" cy=\"275.0\" r=\"10.0\" /><rect x=\"16444.74499999997\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16464.74499999997\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16504.74499999997\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16544.50587890622\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.046π)</text><circle cx=\"16624.26675781247\" cy=\"175.0\" r=\"10.0\" /><rect x=\"16604.26675781247\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16624.26675781247\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16664.26675781247\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16704.02763671872\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.083π)</text><circle cx=\"16783.788515624972\" cy=\"275.0\" r=\"10.0\" /><rect x=\"16763.788515624972\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16783.788515624972\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16823.788515624972\" y=\"305.0\" width=\"71.735625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16859.656328124973\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.05π)</text><circle cx=\"16935.524140624973\" cy=\"225.0\" r=\"10.0\" /><rect x=\"16915.524140624973\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"16935.524140624973\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"16975.524140624973\" y=\"305.0\" width=\"71.735625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17011.391953124974\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.03π)</text><circle cx=\"17087.259765624975\" cy=\"275.0\" r=\"10.0\" /><rect x=\"17067.259765624975\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17087.259765624975\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"17127.259765624975\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17167.020644531225\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.024π)</text><circle cx=\"17246.781523437476\" cy=\"75.0\" r=\"10.0\" /><rect x=\"17226.781523437476\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17246.781523437476\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"17286.781523437476\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17326.542402343726\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.056π)</text><circle cx=\"17406.303281249977\" cy=\"275.0\" r=\"10.0\" /><rect x=\"17386.303281249977\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17406.303281249977\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"17446.303281249977\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17486.064160156227\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.015π)</text><circle cx=\"17565.825039062478\" cy=\"225.0\" r=\"10.0\" /><rect x=\"17545.825039062478\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17565.825039062478\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"17605.825039062478\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17647.91697265623\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.005π)</text><circle cx=\"17730.00890624998\" cy=\"275.0\" r=\"10.0\" /><rect x=\"17710.00890624998\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17730.00890624998\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"17770.00890624998\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17812.10083984373\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.004π)</text><circle cx=\"17894.19277343748\" cy=\"175.0\" r=\"10.0\" /><rect x=\"17874.19277343748\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17894.19277343748\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"17934.19277343748\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"17976.28470703123\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.021π)</text><circle cx=\"18058.37664062498\" cy=\"275.0\" r=\"10.0\" /><rect x=\"18038.37664062498\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18058.37664062498\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"18098.37664062498\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18140.468574218732\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.015π)</text><circle cx=\"18222.560507812483\" cy=\"225.0\" r=\"10.0\" /><rect x=\"18202.560507812483\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18222.560507812483\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"18262.560507812483\" y=\"305.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18300.759374999983\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.02π)</text><circle cx=\"18378.958242187484\" cy=\"275.0\" r=\"10.0\" /><rect x=\"18358.958242187484\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18378.958242187484\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"18418.958242187484\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18461.050175781234\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.006π)</text><circle cx=\"18543.142109374985\" cy=\"125.0\" r=\"10.0\" /><rect x=\"18523.142109374985\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18543.142109374985\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"18583.142109374985\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18622.902988281236\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.003π)</text><circle cx=\"18702.663867187486\" cy=\"275.0\" r=\"10.0\" /><rect x=\"18682.663867187486\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18702.663867187486\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"18742.663867187486\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18784.755800781237\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.015π)</text><circle cx=\"18866.847734374987\" cy=\"225.0\" r=\"10.0\" /><rect x=\"18846.847734374987\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18866.847734374987\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"18906.847734374987\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"18948.939667968738\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.024π)</text><circle cx=\"19031.03160156249\" cy=\"275.0\" r=\"10.0\" /><rect x=\"19011.03160156249\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19031.03160156249\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"19071.03160156249\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19113.12353515624\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.026π)</text><circle cx=\"19195.21546874999\" cy=\"175.0\" r=\"10.0\" /><rect x=\"19175.21546874999\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19195.21546874999\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"19235.21546874999\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19277.30740234374\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.074π)</text><circle cx=\"19359.39933593749\" cy=\"275.0\" r=\"10.0\" /><rect x=\"19339.39933593749\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19359.39933593749\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"19399.39933593749\" y=\"305.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19441.49126953124\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.075π)</text><circle cx=\"19523.583203124992\" cy=\"225.0\" r=\"10.0\" /><rect x=\"19503.583203124992\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19523.583203124992\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"19563.583203124992\" y=\"305.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19601.782070312493\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.04π)</text><circle cx=\"19679.980937499993\" cy=\"275.0\" r=\"10.0\" /><rect x=\"19659.980937499993\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19679.980937499993\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"19719.980937499993\" y=\"305.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19759.741816406244\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.001π)</text><circle cx=\"19839.502695312494\" cy=\"25.0\" r=\"10.0\" /><rect x=\"19819.502695312494\" y=\"305.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19839.502695312494\" y=\"325.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><circle cx=\"19899.502695312494\" cy=\"325.0\" r=\"10.0\" /><rect x=\"19879.502695312494\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19899.502695312494\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"19939.502695312494\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"19981.594628906245\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.013π)</text><circle cx=\"20063.686562499995\" cy=\"275.0\" r=\"10.0\" /><rect x=\"20043.686562499995\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20063.686562499995\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"20103.686562499995\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20145.778496093746\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.027π)</text><circle cx=\"20227.870429687497\" cy=\"325.0\" r=\"10.0\" /><rect x=\"20207.870429687497\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20227.870429687497\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"20267.870429687497\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20309.962363281247\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.036π)</text><circle cx=\"20392.054296874998\" cy=\"225.0\" r=\"10.0\" /><rect x=\"20372.054296874998\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20392.054296874998\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"20432.054296874998\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20474.14623046875\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.072π)</text><circle cx=\"20556.2381640625\" cy=\"325.0\" r=\"10.0\" /><rect x=\"20536.2381640625\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20556.2381640625\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"20596.2381640625\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20638.33009765625\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.018π)</text><circle cx=\"20720.42203125\" cy=\"275.0\" r=\"10.0\" /><rect x=\"20700.42203125\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20720.42203125\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"20760.42203125\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20802.51396484375\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.036π)</text><circle cx=\"20884.6058984375\" cy=\"325.0\" r=\"10.0\" /><rect x=\"20864.6058984375\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20884.6058984375\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"20924.6058984375\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"20964.366777343752\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.067π)</text><circle cx=\"21044.127656250002\" cy=\"175.0\" r=\"10.0\" /><rect x=\"21024.127656250002\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21044.127656250002\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"21084.127656250002\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21123.888535156253\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.003π)</text><circle cx=\"21203.649414062504\" cy=\"325.0\" r=\"10.0\" /><rect x=\"21183.649414062504\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21203.649414062504\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"21243.649414062504\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21285.741347656254\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.017π)</text><circle cx=\"21367.833281250005\" cy=\"275.0\" r=\"10.0\" /><rect x=\"21347.833281250005\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21367.833281250005\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"21407.833281250005\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21449.925214843755\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.001π)</text><circle cx=\"21532.017148437506\" cy=\"325.0\" r=\"10.0\" /><rect x=\"21512.017148437506\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21532.017148437506\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"21572.017148437506\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21614.109082031257\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.004π)</text><circle cx=\"21696.201015625007\" cy=\"225.0\" r=\"10.0\" /><rect x=\"21676.201015625007\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21696.201015625007\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"21736.201015625007\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21775.961894531258\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.009π)</text><circle cx=\"21855.72277343751\" cy=\"325.0\" r=\"10.0\" /><rect x=\"21835.72277343751\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21855.72277343751\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"21895.72277343751\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"21937.81470703126\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.002π)</text><circle cx=\"22019.90664062501\" cy=\"275.0\" r=\"10.0\" /><rect x=\"21999.90664062501\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22019.90664062501\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"22059.90664062501\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22101.99857421876\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.012π)</text><circle cx=\"22184.09050781251\" cy=\"325.0\" r=\"10.0\" /><rect x=\"22164.09050781251\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22184.09050781251\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"22224.09050781251\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22263.85138671876\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.023π)</text><circle cx=\"22343.61226562501\" cy=\"125.0\" r=\"10.0\" /><rect x=\"22323.61226562501\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22343.61226562501\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"22383.61226562501\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22423.373144531262\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.007π)</text><circle cx=\"22503.134023437513\" cy=\"325.0\" r=\"10.0\" /><rect x=\"22483.134023437513\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22503.134023437513\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"22543.134023437513\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22582.894902343764\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.012π)</text><circle cx=\"22662.655781250014\" cy=\"275.0\" r=\"10.0\" /><rect x=\"22642.655781250014\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22662.655781250014\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"22702.655781250014\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22744.747714843765\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.026π)</text><circle cx=\"22826.839648437515\" cy=\"325.0\" r=\"10.0\" /><rect x=\"22806.839648437515\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22826.839648437515\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"22866.839648437515\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22906.600527343766\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.007π)</text><circle cx=\"22986.361406250016\" cy=\"225.0\" r=\"10.0\" /><rect x=\"22966.361406250016\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"22986.361406250016\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23026.361406250016\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23066.122285156267\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.012π)</text><circle cx=\"23145.883164062518\" cy=\"325.0\" r=\"10.0\" /><rect x=\"23125.883164062518\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23145.883164062518\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23185.883164062518\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23227.97509765627\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.024π)</text><circle cx=\"23310.06703125002\" cy=\"275.0\" r=\"10.0\" /><rect x=\"23290.06703125002\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23310.06703125002\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23350.06703125002\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23389.82791015627\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.007π)</text><circle cx=\"23469.58878906252\" cy=\"325.0\" r=\"10.0\" /><rect x=\"23449.58878906252\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23469.58878906252\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23509.58878906252\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23549.34966796877\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.006π)</text><circle cx=\"23629.11054687502\" cy=\"175.0\" r=\"10.0\" /><rect x=\"23609.11054687502\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23629.11054687502\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23669.11054687502\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23711.20248046877\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.026π)</text><circle cx=\"23793.294414062522\" cy=\"325.0\" r=\"10.0\" /><rect x=\"23773.294414062522\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23793.294414062522\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23833.294414062522\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23875.386347656273\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.012π)</text><circle cx=\"23957.478281250023\" cy=\"275.0\" r=\"10.0\" /><rect x=\"23937.478281250023\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"23957.478281250023\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"23997.478281250023\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24037.239160156274\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.022π)</text><circle cx=\"24117.000039062525\" cy=\"325.0\" r=\"10.0\" /><rect x=\"24097.000039062525\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24117.000039062525\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"24157.000039062525\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24199.091972656275\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.023π)</text><circle cx=\"24281.183906250026\" cy=\"225.0\" r=\"10.0\" /><rect x=\"24261.183906250026\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24281.183906250026\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"24321.183906250026\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24363.275839843776\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.005π)</text><circle cx=\"24445.367773437527\" cy=\"325.0\" r=\"10.0\" /><rect x=\"24425.367773437527\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24445.367773437527\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"24485.367773437527\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24525.128652343778\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.012π)</text><circle cx=\"24604.889531250028\" cy=\"275.0\" r=\"10.0\" /><rect x=\"24584.889531250028\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24604.889531250028\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"24644.889531250028\" y=\"355.0\" width=\"71.735625\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24680.75734375003\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.01π)</text><circle cx=\"24756.62515625003\" cy=\"325.0\" r=\"10.0\" /><rect x=\"24736.62515625003\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24756.62515625003\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"24796.62515625003\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24836.38603515628\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.023π)</text><circle cx=\"24916.14691406253\" cy=\"75.0\" r=\"10.0\" /><rect x=\"24896.14691406253\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24916.14691406253\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"24956.14691406253\" y=\"355.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"24994.34578125003\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.04π)</text><circle cx=\"25072.54464843753\" cy=\"325.0\" r=\"10.0\" /><rect x=\"25052.54464843753\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25072.54464843753\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"25112.54464843753\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25152.305527343782\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.047π)</text><circle cx=\"25232.066406250033\" cy=\"275.0\" r=\"10.0\" /><rect x=\"25212.066406250033\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25232.066406250033\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"25272.066406250033\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25314.158339843783\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.007π)</text><circle cx=\"25396.250273437534\" cy=\"325.0\" r=\"10.0\" /><rect x=\"25376.250273437534\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25396.250273437534\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"25436.250273437534\" y=\"355.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25474.449140625034\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.04π)</text><circle cx=\"25552.648007812535\" cy=\"225.0\" r=\"10.0\" /><rect x=\"25532.648007812535\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25552.648007812535\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"25592.648007812535\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25634.739941406286\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.022π)</text><circle cx=\"25716.831875000036\" cy=\"325.0\" r=\"10.0\" /><rect x=\"25696.831875000036\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25716.831875000036\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"25756.831875000036\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25798.923808593787\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.016π)</text><circle cx=\"25881.015742187537\" cy=\"275.0\" r=\"10.0\" /><rect x=\"25861.015742187537\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25881.015742187537\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"25921.015742187537\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"25960.776621093788\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.069π)</text><circle cx=\"26040.53750000004\" cy=\"325.0\" r=\"10.0\" /><rect x=\"26020.53750000004\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26040.53750000004\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"26080.53750000004\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26120.29837890629\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.009π)</text><circle cx=\"26200.05925781254\" cy=\"175.0\" r=\"10.0\" /><rect x=\"26180.05925781254\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26200.05925781254\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"26240.05925781254\" y=\"355.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26278.25812500004\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.01π)</text><circle cx=\"26356.45699218754\" cy=\"325.0\" r=\"10.0\" /><rect x=\"26336.45699218754\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26356.45699218754\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"26396.45699218754\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26436.21787109379\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.012π)</text><circle cx=\"26515.978750000042\" cy=\"275.0\" r=\"10.0\" /><rect x=\"26495.978750000042\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26515.978750000042\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"26555.978750000042\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26595.739628906293\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.005π)</text><circle cx=\"26675.500507812543\" cy=\"325.0\" r=\"10.0\" /><rect x=\"26655.500507812543\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26675.500507812543\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"26715.500507812543\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26757.592441406294\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.008π)</text><circle cx=\"26839.684375000044\" cy=\"225.0\" r=\"10.0\" /><rect x=\"26819.684375000044\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26839.684375000044\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"26879.684375000044\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"26921.776308593795\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.003π)</text><circle cx=\"27003.868242187546\" cy=\"325.0\" r=\"10.0\" /><rect x=\"26983.868242187546\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27003.868242187546\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"27043.868242187546\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27083.629121093796\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.007π)</text><circle cx=\"27163.390000000047\" cy=\"275.0\" r=\"10.0\" /><rect x=\"27143.390000000047\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27163.390000000047\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"27203.390000000047\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27243.150878906297\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.007π)</text><circle cx=\"27322.911757812548\" cy=\"325.0\" r=\"10.0\" /><rect x=\"27302.911757812548\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27322.911757812548\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"27362.911757812548\" y=\"355.0\" width=\"83.1513671875\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27404.487441406298\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.011π)</text><circle cx=\"27486.063125000048\" cy=\"125.0\" r=\"10.0\" /><rect x=\"27466.063125000048\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27486.063125000048\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"27526.063125000048\" y=\"355.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27564.26199218755\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.03π)</text><circle cx=\"27642.46085937505\" cy=\"325.0\" r=\"10.0\" /><rect x=\"27622.46085937505\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27642.46085937505\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"27682.46085937505\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27724.5527929688\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.001π)</text><circle cx=\"27806.64472656255\" cy=\"275.0\" r=\"10.0\" /><rect x=\"27786.64472656255\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27806.64472656255\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"27846.64472656255\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27886.4056054688\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.015π)</text><circle cx=\"27966.16648437505\" cy=\"325.0\" r=\"10.0\" /><rect x=\"27946.16648437505\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"27966.16648437505\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28006.16648437505\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28048.258417968802\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.002π)</text><circle cx=\"28130.350351562553\" cy=\"225.0\" r=\"10.0\" /><rect x=\"28110.350351562553\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28130.350351562553\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28170.350351562553\" y=\"355.0\" width=\"78.4892578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28209.594980468803\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.011π)</text><circle cx=\"28288.839609375053\" cy=\"325.0\" r=\"10.0\" /><rect x=\"28268.839609375053\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28288.839609375053\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28328.839609375053\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28368.600488281303\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.013π)</text><circle cx=\"28448.361367187554\" cy=\"275.0\" r=\"10.0\" /><rect x=\"28428.361367187554\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28448.361367187554\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28488.361367187554\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28528.122246093804\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.004π)</text><circle cx=\"28607.883125000055\" cy=\"325.0\" r=\"10.0\" /><rect x=\"28587.883125000055\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28607.883125000055\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28647.883125000055\" y=\"355.0\" width=\"76.397734375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28686.081992187555\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.01π)</text><circle cx=\"28764.280859375056\" cy=\"175.0\" r=\"10.0\" /><rect x=\"28744.280859375056\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28764.280859375056\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28804.280859375056\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28844.041738281307\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.037π)</text><circle cx=\"28923.802617187557\" cy=\"325.0\" r=\"10.0\" /><rect x=\"28903.802617187557\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"28923.802617187557\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"28963.802617187557\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29003.563496093808\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.006π)</text><circle cx=\"29083.32437500006\" cy=\"275.0\" r=\"10.0\" /><rect x=\"29063.32437500006\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29083.32437500006\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"29123.32437500006\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29165.41630859381\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.014π)</text><circle cx=\"29247.50824218756\" cy=\"325.0\" r=\"10.0\" /><rect x=\"29227.50824218756\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29247.50824218756\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"29287.50824218756\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29327.26912109381\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.031π)</text><circle cx=\"29407.03000000006\" cy=\"225.0\" r=\"10.0\" /><rect x=\"29387.03000000006\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29407.03000000006\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"29447.03000000006\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29489.12193359381\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.006π)</text><circle cx=\"29571.213867187562\" cy=\"325.0\" r=\"10.0\" /><rect x=\"29551.213867187562\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29571.213867187562\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"29611.213867187562\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29653.305800781312\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.006π)</text><circle cx=\"29735.397734375063\" cy=\"275.0\" r=\"10.0\" /><rect x=\"29715.397734375063\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29735.397734375063\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"29775.397734375063\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29817.489667968814\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.017π)</text><circle cx=\"29899.581601562564\" cy=\"325.0\" r=\"10.0\" /><rect x=\"29879.581601562564\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29899.581601562564\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"29939.581601562564\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"29981.673535156315\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.031π)</text><circle cx=\"30063.765468750065\" cy=\"25.0\" r=\"10.0\" /><rect x=\"30043.765468750065\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30063.765468750065\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"30103.765468750065\" y=\"355.0\" width=\"75.365234375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30141.448085937565\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.11π)</text><circle cx=\"30219.130703125065\" cy=\"325.0\" r=\"10.0\" /><rect x=\"30199.130703125065\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30219.130703125065\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"30259.130703125065\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30298.891582031316\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.005π)</text><circle cx=\"30378.652460937567\" cy=\"275.0\" r=\"10.0\" /><rect x=\"30358.652460937567\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30378.652460937567\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"30418.652460937567\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30458.413339843817\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.003π)</text><circle cx=\"30538.174218750068\" cy=\"325.0\" r=\"10.0\" /><rect x=\"30518.174218750068\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30538.174218750068\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"30578.174218750068\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30617.93509765632\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.042π)</text><circle cx=\"30697.69597656257\" cy=\"225.0\" r=\"10.0\" /><rect x=\"30677.69597656257\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30697.69597656257\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"30737.69597656257\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30777.45685546882\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.079π)</text><circle cx=\"30857.21773437507\" cy=\"325.0\" r=\"10.0\" /><rect x=\"30837.21773437507\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30857.21773437507\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"30897.21773437507\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"30939.30966796882\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.005π)</text><circle cx=\"31021.40160156257\" cy=\"275.0\" r=\"10.0\" /><rect x=\"31001.40160156257\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31021.40160156257\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"31061.40160156257\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31101.16248046882\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.028π)</text><circle cx=\"31180.923359375072\" cy=\"325.0\" r=\"10.0\" /><rect x=\"31160.923359375072\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31180.923359375072\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"31220.923359375072\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31263.015292968823\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.042π)</text><circle cx=\"31345.107226562573\" cy=\"175.0\" r=\"10.0\" /><rect x=\"31325.107226562573\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31345.107226562573\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"31385.107226562573\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31424.868105468824\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.021π)</text><circle cx=\"31504.628984375075\" cy=\"325.0\" r=\"10.0\" /><rect x=\"31484.628984375075\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31504.628984375075\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"31544.628984375075\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31584.389863281325\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.009π)</text><circle cx=\"31664.150742187576\" cy=\"275.0\" r=\"10.0\" /><rect x=\"31644.150742187576\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31664.150742187576\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"31704.150742187576\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31746.242675781326\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.023π)</text><circle cx=\"31828.334609375077\" cy=\"325.0\" r=\"10.0\" /><rect x=\"31808.334609375077\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31828.334609375077\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"31868.334609375077\" y=\"355.0\" width=\"78.4892578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31907.579238281327\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.011π)</text><circle cx=\"31986.823867187577\" cy=\"225.0\" r=\"10.0\" /><rect x=\"31966.823867187577\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"31986.823867187577\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32026.823867187577\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32068.915800781328\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.002π)</text><circle cx=\"32151.007734375078\" cy=\"325.0\" r=\"10.0\" /><rect x=\"32131.007734375078\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32151.007734375078\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32191.007734375078\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32233.09966796883\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.021π)</text><circle cx=\"32315.19160156258\" cy=\"275.0\" r=\"10.0\" /><rect x=\"32295.19160156258\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32315.19160156258\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32355.19160156258\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32394.95248046883\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.004π)</text><circle cx=\"32474.71335937508\" cy=\"325.0\" r=\"10.0\" /><rect x=\"32454.71335937508\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32474.71335937508\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32514.71335937508\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32554.47423828133\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.002π)</text><circle cx=\"32634.23511718758\" cy=\"125.0\" r=\"10.0\" /><rect x=\"32614.23511718758\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32634.23511718758\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32674.23511718758\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32713.995996093832\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.018π)</text><circle cx=\"32793.75687500008\" cy=\"325.0\" r=\"10.0\" /><rect x=\"32773.75687500008\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32793.75687500008\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32833.75687500008\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32875.84880859383\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.019π)</text><circle cx=\"32957.94074218758\" cy=\"275.0\" r=\"10.0\" /><rect x=\"32937.94074218758\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"32957.94074218758\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"32997.94074218758\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33037.70162109383\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.003π)</text><circle cx=\"33117.46250000008\" cy=\"325.0\" r=\"10.0\" /><rect x=\"33097.46250000008\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33117.46250000008\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"33157.46250000008\" y=\"355.0\" width=\"42.61453125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33178.76976562508\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0)</text><circle cx=\"33240.07703125008\" cy=\"225.0\" r=\"10.0\" /><rect x=\"33220.07703125008\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33240.07703125008\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"33280.07703125008\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33322.16896484383\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.006π)</text><circle cx=\"33404.260898437584\" cy=\"325.0\" r=\"10.0\" /><rect x=\"33384.260898437584\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33404.260898437584\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"33444.260898437584\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33484.021777343834\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.001π)</text><circle cx=\"33563.782656250085\" cy=\"275.0\" r=\"10.0\" /><rect x=\"33543.782656250085\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33563.782656250085\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"33603.782656250085\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33645.874589843836\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.015π)</text><circle cx=\"33727.966523437586\" cy=\"325.0\" r=\"10.0\" /><rect x=\"33707.966523437586\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33727.966523437586\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"33767.966523437586\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33807.72740234384\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.019π)</text><circle cx=\"33887.48828125009\" cy=\"175.0\" r=\"10.0\" /><rect x=\"33867.48828125009\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33887.48828125009\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"33927.48828125009\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"33967.24916015634\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.051π)</text><circle cx=\"34047.01003906259\" cy=\"325.0\" r=\"10.0\" /><rect x=\"34027.01003906259\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34047.01003906259\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"34087.01003906259\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34126.77091796884\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.004π)</text><circle cx=\"34206.53179687509\" cy=\"275.0\" r=\"10.0\" /><rect x=\"34186.53179687509\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34206.53179687509\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"34246.53179687509\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34288.62373046884\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.045π)</text><circle cx=\"34370.71566406259\" cy=\"325.0\" r=\"10.0\" /><rect x=\"34350.71566406259\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34370.71566406259\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"34410.71566406259\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34450.47654296884\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.029π)</text><circle cx=\"34530.23742187509\" cy=\"225.0\" r=\"10.0\" /><rect x=\"34510.23742187509\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34530.23742187509\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"34570.23742187509\" y=\"355.0\" width=\"78.4892578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34609.48205078134\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.011π)</text><circle cx=\"34688.72667968759\" cy=\"325.0\" r=\"10.0\" /><rect x=\"34668.72667968759\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34688.72667968759\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"34728.72667968759\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34770.81861328134\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.035π)</text><circle cx=\"34852.91054687509\" cy=\"275.0\" r=\"10.0\" /><rect x=\"34832.91054687509\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34852.91054687509\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"34892.91054687509\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"34935.002480468844\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.018π)</text><circle cx=\"35017.094414062594\" cy=\"325.0\" r=\"10.0\" /><rect x=\"34997.094414062594\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35017.094414062594\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"35057.094414062594\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35096.855292968845\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.002π)</text><circle cx=\"35176.616171875095\" cy=\"75.0\" r=\"10.0\" /><rect x=\"35156.616171875095\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35176.616171875095\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"35216.616171875095\" y=\"355.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35256.377050781346\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.016π)</text><circle cx=\"35336.1379296876\" cy=\"325.0\" r=\"10.0\" /><rect x=\"35316.1379296876\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35336.1379296876\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"35376.1379296876\" y=\"355.0\" width=\"84.18386718750001\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35418.22986328135\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(-0.039π)</text><circle cx=\"35500.3217968751\" cy=\"275.0\" r=\"10.0\" /><rect x=\"35480.3217968751\" y=\"355.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"35500.3217968751\" y=\"375.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">X</text><rect x=\"35540.3217968751\" 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      ],
      "text/plain": [
       "<cirq.contrib.svg.svg.SVGCircuit at 0x7f96e6f46190>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SVGCircuit(x_train_circ[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mWZ24w1Oojhk"
   },
   "source": [
    "Convert these `Cirq` circuits to tensors for `tfq`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "IZStEMk4ojhk",
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_train_tfcirc = tfq.convert_to_tensor(x_train_circ)\n",
    "x_test_tfcirc = tfq.convert_to_tensor(x_test_circ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4USiqeOqGL67"
   },
   "source": [
    "## 2. Quantum neural network\n",
    "\n",
    "There is little guidance for a quantum circuit structure that classifies images. Since the classification is based on the expectation of the readout qubit, <a href=\"https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.032308\" class=\"external\">Schuld et al.</a> propose using a combintation of single and two qubit gates, with the configuration dependent upon the block number \"r\". "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helper functions for Tensorboard.\n",
    "\n",
    "\n",
    "- The integer values of samples, so that you can create histograms of the distribution.\n",
    "- The linear XEB fidelity estimate of a set of samples, to give some indication of how \"truly quantum random\" the samples are.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def bits_to_ints(bits):\n",
    "    \"\"\"Convert tensor of bitstrings to tensor of ints.\"\"\"\n",
    "    sigs = tf.constant([1 << i for i in range(N_QUBITS)], dtype=tf.int32)\n",
    "    rounded_bits = tf.clip_by_value(tf.math.round(\n",
    "        tf.cast(bits, dtype=tf.dtypes.float32)), clip_value_min=0, clip_value_max=1)\n",
    "    return tf.einsum('jk,k->j', tf.cast(rounded_bits, dtype=tf.dtypes.int32), sigs)\n",
    "\n",
    "@tf.function\n",
    "def xeb_fid(bits):\n",
    "    \"\"\"Compute linear XEB fidelity of bitstrings.\"\"\"\n",
    "    final_probs = tf.squeeze(\n",
    "        tf.abs(tfq.layers.State()(REFERENCE_CIRCUIT).to_tensor()) ** 2)\n",
    "    nums = bits_to_ints(bits)\n",
    "    return (2 ** N_QUBITS) * tf.reduce_mean(tf.gather(final_probs, nums)) - 1.0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "knIzawEeojho"
   },
   "source": [
    "### 2.1 Build the model circuit\n",
    "\n",
    "This following example shows this layered approach. Each layer uses *n* instances of x,y,z rotational gates along with *n* instances of the same two qubit gate, with each of the data qubits acting on the readout qubit.\n",
    "**We're still working on obtaining a proper dropout model.**\n",
    "Start with a simple class that will add a layer of these gates to a circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-hjxxgU5ojho",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys([cirq.X, cirq.XX, cirq.Y, cirq.YY, cirq.Z, cirq.ZZ, cirq.H, cirq.CZ, cirq.CNOT, cirq.SWAP, cirq.ISWAP, cirq.PhasedXPowGate(phase_exponent=0.123), cirq.PhasedISwapPowGate(phase_exponent=0.123), cirq.FSimGate(theta=0.123, phi=0.456), cirq.I])\n",
      "dict_keys([cirq.depolarize(p=0.01), cirq.asymmetric_depolarize(error_probabilities={'I': 0.94, 'X': 0.01, 'Y': 0.02, 'Z': 0.03}), cirq.generalized_amplitude_damp(p=0.01,gamma=0.02), cirq.amplitude_damp(gamma=0.01), cirq.ResetChannel(), cirq.phase_damp(gamma=0.01), cirq.phase_flip(p=0.01), cirq.bit_flip(p=0.01)])\n"
     ]
    }
   ],
   "source": [
    "print(tfq.util.get_supported_gates().keys())\n",
    "print(tfq.util.get_supported_channels().keys())\n",
    "\n",
    "class CircuitLayerBuilder():\n",
    "    def __init__(self, circuit, data_qubits, repeat_dropout=0, overlap_dropout=False):\n",
    "        \n",
    "        self.data_qubits = data_qubits\n",
    "        self.curr_layer_id = 0\n",
    "        self.circuit = circuit\n",
    "        \n",
    "        self.dropped_out_qubit_ids = []\n",
    "        self.dropout_blacklist = []\n",
    "        \n",
    "        self.overlap_dropout = overlap_dropout\n",
    "        \n",
    "        if repeat_dropout < 1:\n",
    "            repeat_dropout = 1\n",
    "        if overlap_dropout:\n",
    "            for _ in range(repeat_dropout - 1):\n",
    "                # We will be dequeing from this on each rebuild;\n",
    "                # so, each qubit will be in the list for repeat_dropout rebuilds.\n",
    "                self.dropped_out_qubit_ids.append(len(self.data_qubits))\n",
    "            self.delay_next_dropout = 1\n",
    "        else:\n",
    "            # if not overlapping, delay for as long as we're repeating\n",
    "            self.delay_next_dropout = repeat_dropout\n",
    "            \n",
    "        self.delay_next_dropout_i = 0 # try to dropout immediately\n",
    "        \n",
    "        # maps str(symbol) to (is_dropped_out, weight)\n",
    "        self.symbol_map = {}\n",
    "        \n",
    "        self.drop_out_applied = False\n",
    "        \n",
    "    def rebuild(self, circuit, data_qubits, computed_weights, preserve_dropout=False):\n",
    "        # prev_weights is the result of get_weights from the prior epoch.\n",
    "        \n",
    "        self.data_qubits = data_qubits\n",
    "        self.curr_layer_id = 0\n",
    "        self.circuit = circuit\n",
    "        \n",
    "        if preserve_dropout:\n",
    "            if self.overlap_dropout and len(self.dropped_out_qubit_ids) > 0 and self.drop_out_applied:\n",
    "                # Dropping first element. This is either padding, or an actual id that we want to stop dropping out from here on.\n",
    "                dropped_id = self.dropped_out_qubit_ids.pop(0)\n",
    "                self.dropout_blacklist.append(dropped_id)\n",
    "        else:\n",
    "            self.dropout_blacklist = []\n",
    "            self.dropped_out_qubit_ids = []\n",
    "        \n",
    "        if self.delay_next_dropout_i > 0:\n",
    "            self.delay_next_dropout_i -= 1\n",
    "        \n",
    "        if self.delay_next_dropout_i == 0 and not self.overlap_dropout:\n",
    "            # Dropout finished for this qubit!\n",
    "            assert len(self.dropped_out_qubit_ids) <= 1\n",
    "            if len(self.dropped_out_qubit_ids) == 1:\n",
    "                self.dropout_blacklist.append(self.dropped_out_qubit_ids[0])\n",
    "            self.dropped_out_qubit_ids = []\n",
    "        \n",
    "        self.drop_out_applied = False\n",
    "        \n",
    "        #print('self.dropped_out_qubit_ids = ')\n",
    "        #print(self.dropped_out_qubit_ids)\n",
    "        \n",
    "        j = 0\n",
    "        \n",
    "        #print('Rebuilding; prev self.symbol_map:')\n",
    "        #print(self.symbol_map)\n",
    "        \n",
    "        for k in sorted(self.symbol_map.keys()):\n",
    "            prev_is_dropped_out, _ = self.symbol_map[k]\n",
    "            if not prev_is_dropped_out:\n",
    "                # Re-use the prev weight. This isn't directly used as TFQ inputs, but we later use it to generate\n",
    "                # sane inputs for set_weights().\n",
    "                # Also, is-dropped-out is True by default to handle the case when a rebuilt circuit might not add a layer for some reason\n",
    "                self.symbol_map[k] = (True, computed_weights[j])\n",
    "\n",
    "                # prev_weights is a list that only has entries for non-dropped-out elems\n",
    "                j += 1\n",
    "                \n",
    "        #print('Rebuilding done; updated self.symbol_map:')\n",
    "        #print(self.symbol_map)\n",
    "    \n",
    "    def add_param_gate(self, gate, symbol, i, qubit):\n",
    "        if str(symbol) in self.symbol_map:\n",
    "            _, weight = self.symbol_map[str(symbol)]\n",
    "        else:\n",
    "            # default value for weight is 0\n",
    "            weight = 0\n",
    "\n",
    "        if i in self.dropped_out_qubit_ids:\n",
    "            print(\"Dropped out qubit id \" + str(i))\n",
    "            self.symbol_map[str(symbol)] = (True, weight)\n",
    "            self.drop_out_applied = True\n",
    "        else:\n",
    "            self.symbol_map[str(symbol)] = (False, weight)\n",
    "            self.circuit.append(gate(symbol)(qubit))\n",
    "    \n",
    "    def add_controlled_param_pow_gate(self, gate, symbol, i, j, qubit1, qubit2):\n",
    "        if str(symbol) in self.symbol_map:\n",
    "            _, weight = self.symbol_map[str(symbol)]\n",
    "        else:\n",
    "            # default value for weight is 0\n",
    "            weight = 0\n",
    "\n",
    "        if i in self.dropped_out_qubit_ids or (j is not None and j in self.dropped_out_qubit_ids):\n",
    "            #print(\"Dropped out qubit id \" + str(i))\n",
    "            self.symbol_map[str(symbol)] = (True, weight)\n",
    "            self.drop_out_applied = True\n",
    "        else:\n",
    "            self.symbol_map[str(symbol)] = (False, weight)\n",
    "            self.circuit.append(gate(qubit1, qubit2)**(symbol))\n",
    "    \n",
    "    def add_layer(self, block=1, apply_dropout=False):\n",
    "        # at most one dropped qubit added per layer\n",
    "        if apply_dropout and self.delay_next_dropout_i == 0:# and self.curr_layer_id > 0:\n",
    "            while True:\n",
    "                rand_id = np.random.randint(1, (len(self.data_qubits)) + 1) # NEVER select qubit 0 since it's readout!\n",
    "                if rand_id >= len(self.data_qubits):\n",
    "                    rand_id = len(self.data_qubits)\n",
    "                # Kinda hacky, blacklist qubits that we dropped out already\n",
    "                if rand_id not in self.dropout_blacklist or rand_id == len(self.data_qubits):\n",
    "                    break\n",
    "            #print('self.dropout_blacklist =')\n",
    "            #print(self.dropout_blacklist)\n",
    "            #print(rand_id)\n",
    "            if rand_id not in self.dropped_out_qubit_ids and rand_id != len(self.data_qubits):\n",
    "                self.dropped_out_qubit_ids.append(rand_id)\n",
    "            if rand_id != len(self.data_qubits):\n",
    "                self.delay_next_dropout_i = self.delay_next_dropout # reset delay if we're actually going to drop out!\n",
    "\n",
    "        for i in range(len(self.data_qubits)):\n",
    "            self.add_param_gate(cirq.rz, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(i)+'_block'+str(block)+'_rz0'), i, self.data_qubits[i])\n",
    "        for i in range(len(self.data_qubits)):\n",
    "            self.add_param_gate(cirq.ry, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(i)+'_block'+str(block)+'_ry'), i, self.data_qubits[i])\n",
    "        for i in range(len(self.data_qubits)):\n",
    "            self.add_param_gate(cirq.rz, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(i)+'_block'+str(block)+'_rz'), i, self.data_qubits[i])\n",
    "\n",
    "        i = None\n",
    "            \n",
    "        target = None\n",
    "        control = None\n",
    "        n = len(self.data_qubits)\n",
    "        for _ in range(int(n/np.gcd(n, block))):\n",
    "            if block > 0 :\n",
    "                if control is None:\n",
    "                    control_idx = 0\n",
    "                    control = self.data_qubits[control_idx]\n",
    "                # determine control\n",
    "                target_idx = (control_idx+len(self.data_qubits)-block)%len(self.data_qubits)\n",
    "                target = self.data_qubits[target_idx]\n",
    "                \n",
    "                symbol = sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(control_idx)+'_block'+str(block)+'_cz')\n",
    "                if str(symbol) in self.symbol_map:\n",
    "                    _, weight = self.symbol_map[str(symbol)]\n",
    "                else:\n",
    "                    # default value for weight is 0\n",
    "                    weight = 0\n",
    "                \n",
    "                # add gate (as per Schuld, \"B. Optimizing the architecture\")\n",
    "                self.add_controlled_param_pow_gate(cirq.CZ, symbol, control_idx, target_idx, control, target)\n",
    "                self.add_param_gate(cirq.rx, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(target_idx)+'_block'+str(block)+'_rx2'), target_idx, target)\n",
    "                control = target\n",
    "                control_idx = target_idx\n",
    "            else:\n",
    "                break # a trimmed circuit doesn't include entanglements\n",
    "\n",
    "        self.curr_layer_id += 1\n",
    "    \n",
    "    def add_final_out(self):\n",
    "        # Add final learnable operation on qubit 0\n",
    "        i = 0\n",
    "        self.add_param_gate(cirq.rz, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(i)+'_rz0'), i, self.data_qubits[i])\n",
    "        self.add_param_gate(cirq.ry, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(i)+'_ry'), i, self.data_qubits[i])\n",
    "        self.add_param_gate(cirq.rz, sympy.Symbol('s_l'+str(self.curr_layer_id)+'_q'+str(i)+'_rz'), i, self.data_qubits[i])\n",
    "        self.curr_layer_id += 1\n",
    "    \n",
    "    def get_builder_weights(self):\n",
    "        # returns symbol names in sorted order, which should match the order used for PQC (kinda hacky and can potentially break later)\n",
    "        # used as the next input for set_weights()\n",
    "        #\n",
    "        # Order of calls:\n",
    "        # tf.fit();\n",
    "        # builder.rebuild(tf.get_weights());\n",
    "        # add_layer()...;\n",
    "        # tf.set_weights(builder.get_builder_weights());\n",
    "        # tf.fit()\n",
    "        weights_list = []\n",
    "        \n",
    "        for k in sorted(self.symbol_map.keys()):\n",
    "            curr_is_dropout, curr_weight = self.symbol_map[k]\n",
    "            if not curr_is_dropout:\n",
    "                weights_list.append(curr_weight)\n",
    "        \n",
    "        return weights_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Sjo5hANFojhr"
   },
   "source": [
    "Build an example circuit layer to see how it looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TEST CELL to make sure CircuitLayerBuilder works properly\n",
    "circuit = cirq.Circuit()\n",
    "demo_builder = CircuitLayerBuilder(circuit=circuit,\n",
    "                                   data_qubits = cirq.GridQubit.rect(4,2))\n",
    "\n",
    "demo_builder.add_layer(block=1)\n",
    "demo_builder.add_layer(block=3)\n",
    "demo_builder.add_final_out()\n",
    "\n",
    "SVGCircuit(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "T-QhPE1pojhu"
   },
   "source": [
    "Now we build the full $r = {1,3,7}$-layered model, matching the data-circuit size, and include the preparation and readout operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JiALbpwRGL69",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def create_quantum_model(apply_dropout=False, n_dropout=5, builder=None, computed_weights_arr=None):\n",
    "    \"\"\"Create a QNN model circuit and readout operation to go along with it.\"\"\"\n",
    "    data_qubits = cirq.GridQubit.rect(4, 2)  # a 4x2 grid.\n",
    "    circuit = cirq.Circuit()\n",
    "    \n",
    "    if builder is None or computed_weights_arr is None:\n",
    "        builder = CircuitLayerBuilder(\n",
    "            circuit=circuit,\n",
    "            data_qubits=data_qubits,\n",
    "            repeat_dropout=n_dropout)\n",
    "        if apply_dropout:\n",
    "            builder.TEST_STATE_N_DROPOUT = n_dropout\n",
    "            builder.TEST_STATE_DROPOUT_ID = np.random.randint(1, len(data_qubits))\n",
    "        else:\n",
    "            builder.TEST_STATE_N_DROPOUT = None\n",
    "    else:\n",
    "        builder.rebuild(circuit, data_qubits, computed_weights_arr, preserve_dropout=apply_dropout)\n",
    "        \n",
    "        if builder.TEST_STATE_N_DROPOUT is not None and builder.TEST_STATE_N_DROPOUT == 0:\n",
    "            builder.TEST_STATE_N_DROPOUT = n_dropout\n",
    "            builder.TEST_STATE_DROPOUT_ID = np.random.randint(1, len(data_qubits))\n",
    "            if builder.TEST_STATE_DROPOUT_ID > len(data_qubits):\n",
    "                builder.TEST_STATE_N_DROPOUT = 0 # retry on next!\n",
    "\n",
    "    # Then add layers\n",
    "    builder.add_layer(block=1)\n",
    "    builder.add_layer(block=3)\n",
    "    builder.add_layer(block=7)\n",
    "    builder.add_final_out()\n",
    "\n",
    "    # Finally, prepare the readout qubit.\n",
    "\n",
    "    #print('builder.TEST_STATE_N_DROPOUT = ', builder.TEST_STATE_N_DROPOUT)\n",
    "    #print('builder.TEST_STATE_DROPOUT_ID = ', builder.TEST_STATE_DROPOUT_ID)\n",
    "    if apply_dropout and builder.TEST_STATE_N_DROPOUT is not None and builder.TEST_STATE_DROPOUT_ID < len(data_qubits):\n",
    "        print('Built model, going to drop out qubit id ', builder.TEST_STATE_DROPOUT_ID)\n",
    "        readouts = [cirq.Z(data_qubits[0]), cirq.Z(data_qubits[builder.TEST_STATE_DROPOUT_ID])]\n",
    "        builder.TEST_STATE_N_DROPOUT -= 1\n",
    "    else:\n",
    "        readouts = [cirq.Z(data_qubits[0])] # without dropout, only one qubit is measured\n",
    "    \n",
    "    return builder, circuit, readouts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2QZvVh7vojhx",
    "tags": []
   },
   "outputs": [
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      ],
      "text/plain": [
       "<cirq.contrib.svg.svg.SVGCircuit at 0x7f96d9aaa430>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, model_circuit, model_readouts = create_quantum_model(apply_dropout=False)\n",
    "SVGCircuit(model_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LY7vbY6yfABE"
   },
   "source": [
    "### 2.2 Wrap the model-circuit in a tfq-keras model\n",
    "\n",
    "Build the Keras model with the quantum components. This model is fed the \"quantum data\", from `x_train_circ`, that encodes the classical data. It uses a *Parametrized Quantum Circuit* layer, `tfq.layers.PQC`, to train the model circuit, on the quantum data.\n",
    "\n",
    "To classify these images, <a href=\"https://arxiv.org/pdf/1802.06002.pdf\" class=\"external\">Farhi et al.</a> proposed taking the expectation of a readout qubit in a parameterized circuit. The expectation returns a value between 1 and -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZYdf_KOxojh0",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "123\n"
     ]
    }
   ],
   "source": [
    "# Build the Keras model.\n",
    "qlayer = tfq.layers.PQC(model_circuit, model_readouts)\n",
    "print(len(qlayer.get_weights()[0]))\n",
    "\n",
    "model = tf.keras.Sequential([\n",
    "    # The input is the data-circuit, encoded as a tf.string\n",
    "    tf.keras.layers.Input(shape=(), dtype=tf.string),\n",
    "    # The PQC layer returns the expected value of the readout gate, range [-1,1].\n",
    "    qlayer,\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jz-FbVc9ojh3"
   },
   "source": [
    "Next, describe the training procedure to the model, using the `compile` method.\n",
    "\n",
    "Since the the expected readout is in the range `[-1,1]`, optimizing the hinge loss is a somewhat natural fit. \n",
    "\n",
    "Note: Another valid approach would be to shift the output range to `[0,1]`, and treat it as the probability the model assigns to class `3`. This could be used with a standard a `tf.losses.BinaryCrossentropy` loss.\n",
    "\n",
    "To use the hinge loss here you need to make two small adjustments. First convert the labels, `y_train_nocon`, from boolean to `[-1,1]`, as expected by the hinge loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "CgMNkC1Fojh5",
    "tags": []
   },
   "outputs": [],
   "source": [
    "y_train_hinge = 2.0*y_train_nocon_256-1.0\n",
    "y_test_hinge = 2.0*y_test-1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5nwnveDiojh7"
   },
   "source": [
    "Second, use a custiom `hinge_accuracy` metric that correctly handles `[-1, 1]` as the `y_true` labels argument. \n",
    "`tf.losses.BinaryAccuracy(threshold=0.0)` expects `y_true` to be a boolean, and so can't be used with hinge loss)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3XKtZ_TEojh8",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def hinge_accuracy(y_true, y_pred):\n",
    "    y_true = tf.squeeze(y_true) > 0.0\n",
    "    y_pred = tf.squeeze(y_pred) > 0.0\n",
    "    result = tf.cast(y_true == y_pred, tf.float32)\n",
    "\n",
    "    return tf.reduce_mean(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "FlpETlLRojiA",
    "tags": []
   },
   "outputs": [],
   "source": [
    "model.compile(\n",
    "    loss=tf.keras.losses.Hinge(),\n",
    "    optimizer=tf.keras.optimizers.Adam(),\n",
    "    metrics=[hinge_accuracy])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jkHq2RstojiC",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_25\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "pqc_24 (PQC)                 (None, 1)                 123       \n",
      "=================================================================\n",
      "Total params: 123\n",
      "Trainable params: 123\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. TensorBoard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "logdir = \"tb_logs/\" + datetime.datetime.now().strftime(\"%Y%m%d-%H%M%S\")\n",
    "file_writer = tf.summary.create_file_writer(logdir + \"/metrics\")\n",
    "file_writer.set_as_default()\n",
    "tensorboard_callback = tf.keras.callbacks.TensorBoard(log_dir=logdir, histogram_freq=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lsuOzDYblA9s"
   },
   "source": [
    "### Train the quantum model\n",
    "\n",
    "Now train the model—this takes about 45 min. If you don't want to wait that long, use a small subset of the data (set `NUM_EXAMPLES=500`, below). This doesn't really affect the model's progress during training (it only has 123 parameters, and doesn't need much data to constrain these). Using fewer examples just ends training earlier (5min), but runs long enough to show that it is making progress in the validation logs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "n8vuQpSLlBV2",
    "tags": []
   },
   "outputs": [],
   "source": [
    "EPOCHS = 10\n",
    "DROPOUT_EPOCHS = 3 # keep qubits dropped out for this num of epochs\n",
    "#BATCH_SIZE = 32\n",
    "BATCH_SIZE = None\n",
    "#NUM_EXAMPLES=None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qJnNG-3JojiI",
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_train_tfcirc_sub = x_train_tfcirc[:NUM_EXAMPLES]\n",
    "y_train_hinge_sub = y_train_hinge[:NUM_EXAMPLES]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QMSdgGC1GL7D"
   },
   "source": [
    "Training this model to convergence should achieve >85% accuracy on the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nDrop out is not implemented in this example\\ndef train_model(apply_dropout=False):\\n    #dropout_backup_flag = False\\n    \\n    # Corresponds to bias term for non-dropout case; also decouples states for dropout case (two measurements)\\n    res_layer = tf.keras.layers.Dense(1)\\n        \\n    hinge_loss = tf.keras.losses.Hinge()\\n    adam_opt = tf.keras.optimizers.Adam()\\n    \\n    num_iters = EPOCHS\\n    \\n    \\n    for i in range(num_iters):        \\n        # HACK - build new quantum circuit for each epoch and copy over the weights from the old one\\n        \\n        # Toggle apply_dropout off on first epoch\\n        #if dropout_backup_flag:\\n        #    apply_dropout = True\\n        #elif i == 0 and apply_dropout:\\n        #    apply_dropout = False\\n        #    dropout_backup_flag = True\\n        \\n        #if i == num_iters-1:\\n            # Never use dropout on the last epoch; we can\\'t get sane results otherwise\\n            # grab the epoch before last too for better results\\n            #dropout_backup_flag = False\\n            #apply_dropout = False\\n        \\n        print(\\'Iteration \\', i)\\n        \\n        if i == 0:\\n            model_builder, model_circuit, model_readouts = create_quantum_model(apply_dropout, DROPOUT_EPOCHS)\\n            qlayer = tfq.layers.PQC(model_circuit, model_readouts)\\n        else:\\n            model_builder, model_circuit, model_readouts = create_quantum_model(apply_dropout, DROPOUT_EPOCHS, model_builder, qlayer.get_weights()[0])\\n            qlayer_new = tfq.layers.PQC(model_circuit, model_readouts,\\n                                        initializer=tf.keras.initializers.Zeros)\\n            curr_l = model_builder.get_builder_weights()\\n            qlayer_new.set_weights([np.array(curr_l, dtype=np.float32)])\\n            qlayer = qlayer_new\\n            \\n        if apply_dropout:\\n            assert len(model_readouts) == 2\\n\\n        model = tf.keras.Sequential([\\n            tf.keras.layers.Input(shape=(), dtype=tf.string),\\n            qlayer,\\n            res_layer\\n        ])\\n        model.compile(\\n            loss=hinge_loss,\\n            optimizer=adam_opt,\\n            metrics=[hinge_accuracy])\\n\\n        # Now fit the model for this epoch\\n        model.fit(\\n              x_train_tfcirc_sub, y_train_hinge_sub,\\n              batch_size=1,\\n              epochs=1,\\n              verbose=1,\\n              callbacks=[tensorboard_callback])\\n        print(\"Training set perf:\")\\n        model.evaluate(x_train_tfcirc_sub, y_train_hinge_sub, batch_size=1)\\n        print(\"Test set perf:\")\\n        model.evaluate(x_test_tfcirc, y_test_hinge, batch_size=1)\\n        print(\\'\\')\\n    \\n    return model\\n'"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Drop out is not implemented in this example\n",
    "def train_model(apply_dropout=False):\n",
    "    #dropout_backup_flag = False\n",
    "    \n",
    "    # Corresponds to bias term for non-dropout case; also decouples states for dropout case (two measurements)\n",
    "    res_layer = tf.keras.layers.Dense(1)\n",
    "        \n",
    "    hinge_loss = tf.keras.losses.Hinge()\n",
    "    adam_opt = tf.keras.optimizers.Adam()\n",
    "    \n",
    "    num_iters = EPOCHS\n",
    "    \n",
    "    \n",
    "    for i in range(num_iters):        \n",
    "        # HACK - build new quantum circuit for each epoch and copy over the weights from the old one\n",
    "        \n",
    "        # Toggle apply_dropout off on first epoch\n",
    "        #if dropout_backup_flag:\n",
    "        #    apply_dropout = True\n",
    "        #elif i == 0 and apply_dropout:\n",
    "        #    apply_dropout = False\n",
    "        #    dropout_backup_flag = True\n",
    "        \n",
    "        #if i == num_iters-1:\n",
    "            # Never use dropout on the last epoch; we can't get sane results otherwise\n",
    "            # grab the epoch before last too for better results\n",
    "            #dropout_backup_flag = False\n",
    "            #apply_dropout = False\n",
    "        \n",
    "        print('Iteration ', i)\n",
    "        \n",
    "        if i == 0:\n",
    "            model_builder, model_circuit, model_readouts = create_quantum_model(apply_dropout, DROPOUT_EPOCHS)\n",
    "            qlayer = tfq.layers.PQC(model_circuit, model_readouts)\n",
    "        else:\n",
    "            model_builder, model_circuit, model_readouts = create_quantum_model(apply_dropout, DROPOUT_EPOCHS, model_builder, qlayer.get_weights()[0])\n",
    "            qlayer_new = tfq.layers.PQC(model_circuit, model_readouts,\n",
    "                                        initializer=tf.keras.initializers.Zeros)\n",
    "            curr_l = model_builder.get_builder_weights()\n",
    "            qlayer_new.set_weights([np.array(curr_l, dtype=np.float32)])\n",
    "            qlayer = qlayer_new\n",
    "            \n",
    "        if apply_dropout:\n",
    "            assert len(model_readouts) == 2\n",
    "\n",
    "        model = tf.keras.Sequential([\n",
    "            tf.keras.layers.Input(shape=(), dtype=tf.string),\n",
    "            qlayer,\n",
    "            res_layer\n",
    "        ])\n",
    "        model.compile(\n",
    "            loss=hinge_loss,\n",
    "            optimizer=adam_opt,\n",
    "            metrics=[hinge_accuracy])\n",
    "\n",
    "        # Now fit the model for this epoch\n",
    "        model.fit(\n",
    "              x_train_tfcirc_sub, y_train_hinge_sub,\n",
    "              batch_size=1,\n",
    "              epochs=1,\n",
    "              verbose=1,\n",
    "              callbacks=[tensorboard_callback])\n",
    "        print(\"Training set perf:\")\n",
    "        model.evaluate(x_train_tfcirc_sub, y_train_hinge_sub, batch_size=1)\n",
    "        print(\"Test set perf:\")\n",
    "        model.evaluate(x_test_tfcirc, y_test_hinge, batch_size=1)\n",
    "        print('')\n",
    "    \n",
    "    return model\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "Epoch 1/32\n",
      "500/500 [==============================] - 18s 34ms/step - loss: 0.9597 - hinge_accuracy: 0.5742 - val_loss: 0.9999 - val_hinge_accuracy: 0.3480\n",
      "Epoch 2/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.6481 - hinge_accuracy: 0.6969 - val_loss: 1.0873 - val_hinge_accuracy: 0.3080\n",
      "Epoch 3/32\n",
      "500/500 [==============================] - 17s 34ms/step - loss: 0.4904 - hinge_accuracy: 0.7194 - val_loss: 1.0245 - val_hinge_accuracy: 0.3280\n",
      "Epoch 4/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.4506 - hinge_accuracy: 0.7402 - val_loss: 0.9077 - val_hinge_accuracy: 0.4460\n",
      "Epoch 5/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.4028 - hinge_accuracy: 0.7814 - val_loss: 0.8269 - val_hinge_accuracy: 0.5440\n",
      "Epoch 6/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.3817 - hinge_accuracy: 0.8316 - val_loss: 0.7456 - val_hinge_accuracy: 0.6620\n",
      "Epoch 7/32\n",
      "500/500 [==============================] - 17s 34ms/step - loss: 0.3889 - hinge_accuracy: 0.8719 - val_loss: 0.7678 - val_hinge_accuracy: 0.6260\n",
      "Epoch 8/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.3563 - hinge_accuracy: 0.8459 - val_loss: 0.6353 - val_hinge_accuracy: 0.7320\n",
      "Epoch 9/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.3265 - hinge_accuracy: 0.9033 - val_loss: 0.5896 - val_hinge_accuracy: 0.7600\n",
      "Epoch 10/32\n",
      "500/500 [==============================] - 17s 33ms/step - loss: 0.2545 - hinge_accuracy: 0.9306 - val_loss: 0.5128 - val_hinge_accuracy: 0.8140\n",
      "Epoch 11/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.3065 - hinge_accuracy: 0.9345 - val_loss: 0.4441 - val_hinge_accuracy: 0.8520\n",
      "Epoch 12/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.2418 - hinge_accuracy: 0.9500 - val_loss: 0.4136 - val_hinge_accuracy: 0.8560\n",
      "Epoch 13/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.2373 - hinge_accuracy: 0.9526 - val_loss: 0.3860 - val_hinge_accuracy: 0.8800\n",
      "Epoch 14/32\n",
      "500/500 [==============================] - 17s 34ms/step - loss: 0.2161 - hinge_accuracy: 0.9502 - val_loss: 0.3168 - val_hinge_accuracy: 0.9160\n",
      "Epoch 15/32\n",
      "500/500 [==============================] - 19s 38ms/step - loss: 0.2007 - hinge_accuracy: 0.9531 - val_loss: 0.2982 - val_hinge_accuracy: 0.9280\n",
      "Epoch 16/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.2118 - hinge_accuracy: 0.9384 - val_loss: 0.3127 - val_hinge_accuracy: 0.9060\n",
      "Epoch 17/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.1764 - hinge_accuracy: 0.9684 - val_loss: 0.3039 - val_hinge_accuracy: 0.9060\n",
      "Epoch 18/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.1345 - hinge_accuracy: 0.9760 - val_loss: 0.2833 - val_hinge_accuracy: 0.9160\n",
      "Epoch 19/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.1421 - hinge_accuracy: 0.9760 - val_loss: 0.2499 - val_hinge_accuracy: 0.9320\n",
      "Epoch 20/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.1620 - hinge_accuracy: 0.9705 - val_loss: 0.2959 - val_hinge_accuracy: 0.8960\n",
      "Epoch 21/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.1469 - hinge_accuracy: 0.9689 - val_loss: 0.2058 - val_hinge_accuracy: 0.9480\n",
      "Epoch 22/32\n",
      "500/500 [==============================] - 17s 33ms/step - loss: 0.1604 - hinge_accuracy: 0.9676 - val_loss: 0.2227 - val_hinge_accuracy: 0.9460\n",
      "Epoch 23/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.1730 - hinge_accuracy: 0.9686 - val_loss: 0.2336 - val_hinge_accuracy: 0.9400\n",
      "Epoch 24/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.1474 - hinge_accuracy: 0.9757 - val_loss: 0.2304 - val_hinge_accuracy: 0.9340\n",
      "Epoch 25/32\n",
      "500/500 [==============================] - 17s 34ms/step - loss: 0.1313 - hinge_accuracy: 0.9688 - val_loss: 0.2140 - val_hinge_accuracy: 0.9400\n",
      "Epoch 26/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.1140 - hinge_accuracy: 0.9756 - val_loss: 0.2251 - val_hinge_accuracy: 0.9340\n",
      "Epoch 27/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.1438 - hinge_accuracy: 0.9605 - val_loss: 0.2076 - val_hinge_accuracy: 0.9400\n",
      "Epoch 28/32\n",
      "500/500 [==============================] - 17s 34ms/step - loss: 0.1365 - hinge_accuracy: 0.9788 - val_loss: 0.2125 - val_hinge_accuracy: 0.9360\n",
      "Epoch 29/32\n",
      "500/500 [==============================] - 16s 32ms/step - loss: 0.1025 - hinge_accuracy: 0.9705 - val_loss: 0.2089 - val_hinge_accuracy: 0.9380\n",
      "Epoch 30/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.0929 - hinge_accuracy: 0.9810 - val_loss: 0.1818 - val_hinge_accuracy: 0.9480\n",
      "Epoch 31/32\n",
      "500/500 [==============================] - 16s 33ms/step - loss: 0.0987 - hinge_accuracy: 0.9825 - val_loss: 0.1938 - val_hinge_accuracy: 0.9460\n",
      "Epoch 32/32\n",
      "500/500 [==============================] - 21s 43ms/step - loss: 0.1009 - hinge_accuracy: 0.9659 - val_loss: 0.1959 - val_hinge_accuracy: 0.9420\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7f96dad15d00>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Corresponds to bias term for non-dropout case; also decouples states for dropout case (two measurements)\n",
    "res_layer = tf.keras.layers.Dense(1)\n",
    "\n",
    "hinge_loss = tf.keras.losses.Hinge()\n",
    "adam_opt = tf.keras.optimizers.Adam()\n",
    "    \n",
    "model = tf.keras.Sequential([\n",
    "            tf.keras.layers.Input(shape=(), dtype=tf.string),\n",
    "            qlayer,\n",
    "            res_layer\n",
    "        ])\n",
    "model.compile(\n",
    "    loss=hinge_loss,\n",
    "    optimizer=adam_opt,\n",
    "    metrics=[hinge_accuracy])\n",
    "\n",
    "# Now fit the model for this epoch\n",
    "model.fit(\n",
    "      x_train_tfcirc_sub, y_train_hinge_sub,\n",
    "      batch_size=1,\n",
    "      epochs=32,\n",
    "      verbose=1,\n",
    "      validation_data=(x_test_tfcirc, y_test_hinge),\n",
    "      callbacks=[tensorboard_callback])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Non-dropout training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.2956 - hinge_accuracy: 0.9340\n",
      "Non-dropout test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.4669 - hinge_accuracy: 0.8520\n"
     ]
    }
   ],
   "source": [
    "print(\"Non-dropout training set perf:\")\n",
    "model.evaluate(x_train_tfcirc_sub, y_train_hinge_sub, batch_size=1)\n",
    "print(\"Non-dropout test set perf:\")\n",
    "qnn_results = model.evaluate(x_test_tfcirc, y_test_hinge, batch_size=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're still working on obtaining a proper dropout model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Ya9qP3KkojiM",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration  0\n",
      "Built model, going to drop out qubit id  7\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 12s 23ms/step - loss: 0.9637 - hinge_accuracy: 0.6980\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.8354 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 1.0956 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  1\n",
      "Built model, going to drop out qubit id  7\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 11s 22ms/step - loss: 0.7516 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.6136 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 1.2616 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  2\n",
      "Built model, going to drop out qubit id  7\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 12s 24ms/step - loss: 0.5440 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 12ms/step - loss: 0.5702 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 5s 11ms/step - loss: 1.2612 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  3\n",
      "Built model, going to drop out qubit id  3\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 11s 22ms/step - loss: 0.5702 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.5578 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 1.2169 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  4\n",
      "Built model, going to drop out qubit id  3\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 11s 22ms/step - loss: 0.5018 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.5341 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 12ms/step - loss: 1.1770 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  5\n",
      "Built model, going to drop out qubit id  3\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 11s 22ms/step - loss: 0.4806 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.5094 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 1.0998 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  6\n",
      "Built model, going to drop out qubit id  6\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 11s 22ms/step - loss: 0.4855 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.5056 - hinge_accuracy: 0.7000\n",
      "Test set perf:\n",
      "500/500 [==============================] - 5s 11ms/step - loss: 1.0732 - hinge_accuracy: 0.3000\n",
      "\n",
      "Iteration  7\n",
      "Built model, going to drop out qubit id  6\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 11s 22ms/step - loss: 0.4544 - hinge_accuracy: 0.7334\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 12ms/step - loss: 0.4730 - hinge_accuracy: 0.7040\n",
      "Test set perf:\n",
      "500/500 [==============================] - 5s 11ms/step - loss: 0.9686 - hinge_accuracy: 0.3400\n",
      "\n",
      "Iteration  8\n",
      "Built model, going to drop out qubit id  6\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 12s 24ms/step - loss: 0.4237 - hinge_accuracy: 0.7434\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 12ms/step - loss: 0.4334 - hinge_accuracy: 0.7660\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 12ms/step - loss: 0.8625 - hinge_accuracy: 0.4620\n",
      "\n",
      "Iteration  9\n",
      "Built model, going to drop out qubit id  6\n",
      "WARNING:tensorflow:Model failed to serialize as JSON. Ignoring... Layer PQC has arguments in `__init__` and therefore must override `get_config`.\n",
      "500/500 [==============================] - 12s 23ms/step - loss: 0.3893 - hinge_accuracy: 0.7981\n",
      "Training set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.3937 - hinge_accuracy: 0.8160\n",
      "Test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.7576 - hinge_accuracy: 0.6240\n",
      "\n"
     ]
    }
   ],
   "source": [
    "dropout_model = train_model(apply_dropout=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dropout training set perf:\n",
      "500/500 [==============================] - 6s 12ms/step - loss: 0.3937 - hinge_accuracy: 0.8160\n",
      "Dropout test set perf:\n",
      "500/500 [==============================] - 6s 11ms/step - loss: 0.7576 - hinge_accuracy: 0.6240\n"
     ]
    }
   ],
   "source": [
    "print(\"Dropout training set perf:\")\n",
    "dropout_model.evaluate(x_train_tfcirc_sub, y_train_hinge_sub, batch_size=1)\n",
    "print(\"Dropout test set perf:\")\n",
    "qnn_results = dropout_model.evaluate(x_test_tfcirc, y_test_hinge, batch_size=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3ER7B7aaojiP"
   },
   "source": [
    "Note: The training accuracy reports the average over the epoch. The validation accuracy is evaluated at the end of each epoch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8952YvuWGL7J"
   },
   "source": [
    "## 4. Classical neural network\n",
    "\n",
    "While the quantum neural network works for this simplified MNIST problem, a basic classical neural network can easily outperform a QNN on this task. After a single epoch, a classical neural network can achieve >98% accuracy on the holdout set.\n",
    "\n",
    "In the following example, a classical neural network is used for for the 3-6 classification problem using the entire 28x28 image instead of subsampling the image. This easily converges to nearly 100% accuracy of the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pZofEHhLGL7L",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_16\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_2 (Conv2D)            (None, 26, 26, 32)        320       \n",
      "_________________________________________________________________\n",
      "conv2d_3 (Conv2D)            (None, 24, 24, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "flatten_2 (Flatten)          (None, 9216)              0         \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 128)               1179776   \n",
      "_________________________________________________________________\n",
      "dropout_3 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_5 (Dense)              (None, 1)                 129       \n",
      "=================================================================\n",
      "Total params: 1,198,721\n",
      "Trainable params: 1,198,721\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "def create_classical_model():\n",
    "    # A simple model based off LeNet from https://keras.io/examples/mnist_cnn/\n",
    "    model = tf.keras.Sequential()\n",
    "    model.add(tf.keras.layers.Conv2D(32, [3, 3], activation='relu', input_shape=(28,28,1)))\n",
    "    model.add(tf.keras.layers.Conv2D(64, [3, 3], activation='relu'))\n",
    "    model.add(tf.keras.layers.MaxPooling2D(pool_size=(2, 2)))\n",
    "    model.add(tf.keras.layers.Dropout(0.25))\n",
    "    model.add(tf.keras.layers.Flatten())\n",
    "    model.add(tf.keras.layers.Dense(128, activation='relu'))\n",
    "    model.add(tf.keras.layers.Dropout(0.5))\n",
    "    model.add(tf.keras.layers.Dense(1))\n",
    "    return model\n",
    "\n",
    "\n",
    "model = create_classical_model()\n",
    "model.compile(loss=tf.keras.losses.BinaryCrossentropy(from_logits=True),\n",
    "              optimizer=tf.keras.optimizers.Adam(),\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "CiAJl7sZojiU",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95/95 [==============================] - 19s 188ms/step - loss: 0.1138 - accuracy: 0.9467 - val_loss: 0.0057 - val_accuracy: 0.9990\n",
      "62/62 [==============================] - 1s 13ms/step - loss: 0.0057 - accuracy: 0.9990\n"
     ]
    }
   ],
   "source": [
    "model.fit(x_train,\n",
    "          y_train,\n",
    "          batch_size=128,\n",
    "          epochs=1,\n",
    "          verbose=1,\n",
    "          validation_data=(x_test, y_test))\n",
    "\n",
    "cnn_results = model.evaluate(x_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "X5-5BVJaojiZ"
   },
   "source": [
    "The above model has nearly 1.2M parameters. For a more fair comparison, try a 37-parameter model, on the subsampled images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "70TOM6r-ojiZ",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_17\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "flatten_3 (Flatten)          (None, 16)                0         \n",
      "_________________________________________________________________\n",
      "dense_6 (Dense)              (None, 2)                 34        \n",
      "_________________________________________________________________\n",
      "dense_7 (Dense)              (None, 1)                 3         \n",
      "=================================================================\n",
      "Total params: 37\n",
      "Trainable params: 37\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "def create_fair_classical_model():\n",
    "    # A simple model based off LeNet from https://keras.io/examples/mnist_cnn/\n",
    "    model = tf.keras.Sequential()\n",
    "    model.add(tf.keras.layers.Flatten(input_shape=(4,4,1)))\n",
    "    model.add(tf.keras.layers.Dense(2, activation='relu'))\n",
    "    model.add(tf.keras.layers.Dense(1))\n",
    "    return model\n",
    "\n",
    "\n",
    "model = create_fair_classical_model()\n",
    "model.compile(loss=tf.keras.losses.BinaryCrossentropy(from_logits=True),\n",
    "              optimizer=tf.keras.optimizers.Adam(),\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lA_Fx-8gojid",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "81/81 - 1s - loss: 0.6579 - accuracy: 0.5250 - val_loss: 0.6457 - val_accuracy: 0.4878\n",
      "Epoch 2/20\n",
      "81/81 - 0s - loss: 0.6325 - accuracy: 0.5525 - val_loss: 0.6172 - val_accuracy: 0.5701\n",
      "Epoch 3/20\n",
      "81/81 - 0s - loss: 0.5962 - accuracy: 0.6614 - val_loss: 0.5704 - val_accuracy: 0.7642\n",
      "Epoch 4/20\n",
      "81/81 - 0s - loss: 0.5455 - accuracy: 0.8182 - val_loss: 0.5161 - val_accuracy: 0.8237\n",
      "Epoch 5/20\n",
      "81/81 - 0s - loss: 0.4965 - accuracy: 0.8508 - val_loss: 0.4702 - val_accuracy: 0.8318\n",
      "Epoch 6/20\n",
      "81/81 - 0s - loss: 0.4564 - accuracy: 0.8564 - val_loss: 0.4347 - val_accuracy: 0.8308\n",
      "Epoch 7/20\n",
      "81/81 - 0s - loss: 0.4255 - accuracy: 0.8578 - val_loss: 0.4075 - val_accuracy: 0.8308\n",
      "Epoch 8/20\n",
      "81/81 - 0s - loss: 0.4008 - accuracy: 0.8582 - val_loss: 0.3854 - val_accuracy: 0.8323\n",
      "Epoch 9/20\n",
      "81/81 - 0s - loss: 0.3807 - accuracy: 0.8667 - val_loss: 0.3675 - val_accuracy: 0.8709\n",
      "Epoch 10/20\n",
      "81/81 - 0s - loss: 0.3637 - accuracy: 0.8803 - val_loss: 0.3522 - val_accuracy: 0.8709\n",
      "Epoch 11/20\n",
      "81/81 - 0s - loss: 0.3493 - accuracy: 0.8822 - val_loss: 0.3394 - val_accuracy: 0.8709\n",
      "Epoch 12/20\n",
      "81/81 - 0s - loss: 0.3369 - accuracy: 0.8829 - val_loss: 0.3284 - val_accuracy: 0.8709\n",
      "Epoch 13/20\n",
      "81/81 - 0s - loss: 0.3261 - accuracy: 0.8829 - val_loss: 0.3188 - val_accuracy: 0.8709\n",
      "Epoch 14/20\n",
      "81/81 - 0s - loss: 0.3167 - accuracy: 0.8829 - val_loss: 0.3102 - val_accuracy: 0.8709\n",
      "Epoch 15/20\n",
      "81/81 - 0s - loss: 0.3083 - accuracy: 0.8829 - val_loss: 0.3027 - val_accuracy: 0.8709\n",
      "Epoch 16/20\n",
      "81/81 - 0s - loss: 0.3009 - accuracy: 0.8831 - val_loss: 0.2960 - val_accuracy: 0.8714\n",
      "Epoch 17/20\n",
      "81/81 - 0s - loss: 0.2943 - accuracy: 0.8833 - val_loss: 0.2901 - val_accuracy: 0.8714\n",
      "Epoch 18/20\n",
      "81/81 - 0s - loss: 0.2884 - accuracy: 0.8834 - val_loss: 0.2847 - val_accuracy: 0.8720\n",
      "Epoch 19/20\n",
      "81/81 - 0s - loss: 0.2830 - accuracy: 0.8835 - val_loss: 0.2798 - val_accuracy: 0.8720\n",
      "Epoch 20/20\n",
      "81/81 - 0s - loss: 0.2782 - accuracy: 0.8835 - val_loss: 0.2754 - val_accuracy: 0.8720\n",
      "62/62 [==============================] - 0s 721us/step - loss: 0.2754 - accuracy: 0.8720\n"
     ]
    }
   ],
   "source": [
    "model.fit(x_train_nocon_256,\n",
    "          y_train_nocon_256,\n",
    "          batch_size=128,\n",
    "          epochs=20,\n",
    "          verbose=2,\n",
    "          validation_data=(x_test_bin, y_test))\n",
    "\n",
    "fair_nn_results = model.evaluate(x_test_bin, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RH3mam7EGL7N"
   },
   "source": [
    "## 5. Comparison\n",
    "\n",
    "Higher resolution input and a more powerful model make this problem easy for the CNN. While a classical model of similar power (~32 parameters) trains to a similar accuracy in a fraction of the time. One way or the other, the classical neural network easily outperforms the quantum neural network. For classical data, it is difficult to beat a classical neural network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "NOMeN7pMGL7P",
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rickyyoung/opt/anaconda3/lib/python3.8/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qnn_accuracy = qnn_results[1]\n",
    "cnn_accuracy = cnn_results[1]\n",
    "fair_nn_accuracy = fair_nn_results[1]\n",
    "\n",
    "sns.barplot([\"Quantum\", \"Classical, full\", \"Classical, fair\"],\n",
    "            [qnn_accuracy, cnn_accuracy, fair_nn_accuracy])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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