programs/quine16.fj

// $ fj --asm -w 16 -v 0 quine16.fj -o quine16.fjm && fj --run -s quine16.fjm >/tmp/output && diff quine16.fjm /tmp/output && echo "quine!"
//
// Author: Luis Fernando Estrozi ( https://github.com/lestrozi )
//
//
// It's not always one can say they quite literally understand every bit of a program.
//
//
// ## Quine
// 
// Quine is defined in Wikipedia as "a computer program which takes no input and produces a copy of its own source code as its only output".
//
// The definition of "source code" for FlipJump may be ambiguous, since what FlipJump defines is mainly an op (2 integers) that
// can be represented as text with a separator, in binary, or many other formats.
// 
// I took the liberty to define a Quine for FlipJump as a binary (fjm) that prints itself (including the header struct).
// 
// First, create quine16.fjm from the source:
// `$ fj --asm -w 16 quine16.fj -o quine16.fjm`
//
// Then the quine can be checked using:
// `$ fj --run -s quine16.fjm >output`
// `$ diff quine16.fjm output`
// 
// 
// ## How does it work?
// 
// This is a good starting point to understand how a quine can be done:
// https://www.codingame.com/playgrounds/50485/brainfuck-part-7---quine-some-non-bf-quine-theory/welcome
// 
// In short, we need:
// * A data section that will store the code
// * A way to print the data section contents
// * A way to print the data section as it is defined (because our code also contains the data section,
//   we need to print it as part of the code)
// 
// A naive way to implement a quine in FJ would be to encode the bytes of the code 1 bit at a time, for
// example, to encode 0xAB (0b1010 1011), we could do (lsb):
// 
// data:
// ;digits + dw*1
// ;digits + dw*1
// ;digits + dw*0
// ;digits + dw*1
// ;digits + dw*0
// ;digits + dw*1
// ;digits + dw*0
// ;digits + dw*1
// ;end
// 
// Then we'd need a digits "array", such as:
// 
// digits:
// dw+0;resume
// dw+1;resume
// 
// And a pointer to the current position we're iterating of data:
//
// jmp_data:
//	;data+0*w
//   
// (resume would point to code that increments the pointer to data at jmp_data and jumps to jmp_data)
// 
// This would be using an op (16 + 16 bits) to encode a single bit, which is very wasteful.
// We could encode more bits, but the [digits] array needs to grow accordingly.
//
// For example, encoding 4 bits instead of 1:
// data:
// ;digits + dw*0xB
// ;digits + dw*0xA
// ;end
// 
// Adopting the notation label[i] to represent the address `label + i*dw`, our 
// digits "array" needs to be 16 ops long: digits[0x0] to digits[0xF]. Notice also that
// each of these addresses would need to print 4 bits now, not only a single bit.
// 
// I defined the digits array in a recursive-ish way:
/////////////////////////////////////////////////////
// def digit_jmp addr, i {
//   dw + (i % 2); addr + ((i>>1) * dw)
// }
// 
// digits:
// rep(16, i) .digit_jmp p000, i
// 
// p000:
// rep(8, i) .digit_jmp p00, i
// 
// p00:
// rep(4, i) .digit_jmp p0, i
// 
// p0:
// dw+0;jmp_resume
// dw+1;jmp_resume
/////////////////////////////////////////////////////
// 
// Here, the digits array has 16 entries that will print only the first (lsb) bit of
// the 4 bits and jump to the appropriate p000[n] position to print the other 3 bits.
// In this way, printing "0111" and "0110" becomes either, respectively:
// * print 1; print 110
// * print 0; print 110
// 
// Which means we can re-use the "print 110" for both.
// 
// 
// After this detour about the digits array, let's get back to how data is being encoded.
// Let's say we wanted to encode 0xAB and 0xCD, that's how we'd do:
// data:
// ;digits + dw*0xB
// ;digits + dw*0xA;
// ;digits + dw*0xD;
// ;digits + dw*0xC;
// ;end
// 
// Notice this is still wasteful in the sense that the first 16 bits of each op are unused.
// 
// So let's try to make it denser:
// data:
// 0              ;digits + dw*0xB		// data[0]
// digits + dw*0xA;digits + dw*0xD		// data[1]
// digits + dw*0xC;end				// data[2]
// 
// This doubles the amount of data we can store now if we increment our pointer to data
// 16 bits at a time instead of 32 bits at a time.
// While we'd iterate over the previous encoding as data[0], data[1], data[2], data[3], data[4]; this
// one will be iterated as data[0], data[0]+w, data[1], data[1]+w, data[2].
// 
// The problem is that, when we process, for example, data[1], we'll not only jump to
// (digits + dw*0xD) - which is what we intended - but we'll also have a side effect of flipping (digits + dw*0xA),
// which would mess our digits array.
// 
// The way I'm fixing this is to, before jumping to data[i] (or data[i]+w), flipping a bit of the first word, which
// redirects the flipping from digits to a designed flipping area, where bits can be safely flipped!
// This is confusing, so let's use an example. If data has the values described above, before jumping
// to data[0]+w, we'd have changed it to:
//
// data:
// 0              ;flipping_area + dw*0xB	// <- notice it doesn't point to the digits array anymore
// digits + dw*0xA;digits + dw*0xD
// digits + dw*0xC;end
// 
// Now we're wasting 16 ops in flipping area (because it needs to be the same size as digits), but
// not only it's worth it since we double the data density, there's also a trick to reuse this space later.
// 
// After all that explanation, here's an diagram of how printing the code works:
// 
//                       |
//                       V
//               +---------------+          +------------+
//    +--------> | flip_data_bit | <--------| jmp_resume |
//    |          +---------------+          +------------+
//    |                  |                         ^
//    |                  V                         |
//    |           +------------+          +-----------------+
//    |           | after_flip |          | digits + [char] |
//    |           +------------+          +-----------------+
//    |                  |                         ^
//    |                  |                         |
//    |         +--------+-------+                 |
//    |         |                |                 |
//    |         V                V                 |
//    |      +-----+       +----------+            |
//    +------| inc |       | jmp_data |------------+
//           +-----+       +----------+
//
// `flip_data_bit` also alternates the next jump after `after_flip` between `jmp_data` and `inc` (see the fork above)
//
//  `flip_data_bit` -> `after_flip` -> `jmp_data` -> `digits` -> `jmp_resume`
//        ^                                                            |
//        |                                                            V
//      `inc` <----------- `after_flip` (unflip!) <----------- `flip_data_bit`
// 
//
// After we print the code, we need to print the data definition, which is pretty similar. We need to
// rewind the pointer to data* and start printing again, but this time with some padding before and after.
// * actually we need to rewind it 1 word earlier than data, because we also want to print
// the first word of data.
//
// The shift from printing code to printing data is done by `end_print_code`.
//
// The way `inc` (used to increment the pointer to data) is implemented is also optimized.
// Let's say jmp_data is pointing to data[0]. In the next iteration, we want it to point
// to data[0]+w, so we just need to flip bit (jmp_data+dbit-1) (which is what `inc` does).
//
// This is what happens to jmp_data:
//                                             V
// Before:  0000 0000 0000 0000 ; 0000 1100 0110 0000  (0x0000; 0x0C60)
//  After:  0000 0000 0000 0000 ; 0000 1100 0111 0000  (0x0000; 0x0C70)
//                                             ^
//
// Easy. But the next iteration is more difficult, because flipping bit (jmp_data+dbit-1) overflows,
// so we need to propagate the increment up to 10 bits before this one.
//
// The way I initially did this was like (not tested):
/////////////////////////////////////////////////////
// inc:
//	bit.not counter+0*dw
//	wflip counter+0*dw+w, b4, counter+0*dw
//
// b4:
// 	;handle_overflow_b4
//	;jmp_loop		// b4 is now 1, so no overflow
//
// handle_overflow_b4:
// 	bit.not counter+1*dw
// 	wflip counter+1*dw+w, b5, counter+1*dw
//
// b5:
// 	;handle_overflow_b5
//	;jmp_loop		// b5 is now 1, so no overflow
//
// ...
/////////////////////////////////////////////////////
//
// Notice that `;jmp_loop` repeats for every bit of our incrementer, and `b4` and `b5` just redirects
// to handle_overflow_b4/5. The way I managed to optimize this was to actually make counter[i]
// alternate pointing to the overflow-handler (named b4, b5, b6...) and pointing to the
// `;jmp_loop` (b4_alt, b5_alt, b6_alt...)
//
// I had to place only one additional `;jmp_loop` in the code in order to ensure that all
// wflips [`b5` <-> `b5_alt`], [`b6` <-> `b6_alt`], etc. were single-bit.
//
//
// ## Result
// This 16-bits quine requires only 99 ops (2 of them are padding required to align
// the most efficient position for `data`, considering it needs to be rewinded), plus
// (99*4 + 52 bytes from the header) = 448 ops to store data.
// This means its total size is 99+448 = 547 ops 
//
// I also managed to reuse 16-ops of the `flipping area` because knowing only 1 bit of each op is flipped,
// the "jump" address can still be used (it doesn't get flipped). The only side effect is that bits 0x0000
// and 0x0001 might be flipped while executing that op, but that's not an issue.
// The flip operand of this area was also used for some ops, but doing so required defining the flip
// operand *incorrectly*, so it gets "fixed" in runtime while bits are flipped in this area.
//
//
// Finally, I had to align those labels such that the wflip between them be single-bit
// (ie (label1 XOR label2) must be a power of 2)
// [b5], 			[b5_alt]
// [b6], 			[b6_alt]
// [b7], 			[b7_alt]
// [b8], 			[b8_alt]
// [b9], 			[b9_alt]
// [b10], 			[b10_alt]
// [b11], 			[b11_alt]
// [b12], 			[b12_alt]
// [b13], 			[b13_alt]
// [b14], 			[b14_alt]
// [resume_print_data], 	[flip_data_bit]
// [loop_print_data], 		[flip_data_bit]
// [end], 			[end_print_code]
// [end_1], 			[resume_print_data]
// [end_1], 			[end_cont]
// [print_dwsize_padding]+0x20,	[jmp_resume]
// [print_data_padding]+0x20,	[jmp_resume]
// [inc],			[jmp_data]
//
// [digits] must also be a multiple of 0x200
//
//
// ## Future work
// At first glance you could think this 2244 bytes (compiled) program is the smallest
// possible quine for flip-jump, but it is not.
// I already managed to make it less than 2000 bytes
// (sha256: 6a5c528d0a4a5a79aa15cb12425e56afb84b06cb808fbcc9f0ac53c6d5110f73) and
// I'm pretty sure it can still be improved, but those are small bruteforce marginal
// gains that I'm not too interested in persuing at the moment.


;flip_data_bit
IO:
;0

b5:
	// alternate b6 with b6_alt
	wflip counter+1*dw+w, b6^b6_alt, b5xor

b6:
	// alternate b7 with b7_alt
	wflip counter+2*dw+w, b7^b7_alt, b6xor

b7:
	// alternate b8 with b8_alt
	wflip counter+3*dw+w, b8^b8_alt, b7xor


//////////////////////////////////////////////////
b5xor:
	jmp_data+dbit+0;counter+1*dw
//////////////////////////////////////////////////

b5_alt:
b7_alt:
b8_alt:
b11_alt:
b13_alt:
jmp_loop:
	;flip_data_bit

b8:
	// alternate b9 with b9_alt
	wflip counter+4*dw+w, b9^b9_alt, b8xor

//////////////////////////////////////////////////
b6xor:
	jmp_data+dbit+1;counter+2*dw
//////////////////////////////////////////////////

b9:
	// alternate b10 with b10_alt
	wflip counter+5*dw+w, b10^b10_alt, b9xor


b10:
	// alternate b11 with b11_alt
	wflip counter+6*dw+w, b11^b11_alt, b10xor


b6_alt:
b9_alt:
b10_alt:
b12_alt:
b14_alt:
;jmp_loop

//////////////////////////////////////////////////
b7xor:
	jmp_data+dbit+2;counter+3*dw
//////////////////////////////////////////////////

//////////////////////////////////////////////////
b8xor:
	jmp_data+dbit+3;counter+4*dw
//////////////////////////////////////////////////

b11:
	// alternate b12 with b12_alt
	wflip counter+7*dw+w, b12^b12_alt, b11xor

b12:
	// alternate b13 with b13_alt
	wflip counter+8*dw+w, b13^b13_alt, b12xor

//////////////////////////////////////////////////
b9xor:
	jmp_data+dbit+4;counter+5*dw
//////////////////////////////////////////////////

end_cont:
	dw+0;
	dw+0;
halt:
	dw+0;halt

//////////////////////////////////////////////////
b10xor:
	jmp_data+dbit+5;counter+6*dw
//////////////////////////////////////////////////

//////////////////////////////////////////////////
b11xor:
	jmp_data+dbit+6;counter+7*dw
//////////////////////////////////////////////////

b13:
	// alternate b14 with b14_alt
	wflip counter+9*dw+w, b14^b14_alt, b13xor


//////////////////////////////////////////////////
b12xor:
	jmp_data+dbit+7;counter+8*dw
//////////////////////////////////////////////////

end:
	// print 0x8 (using the digits array) and return to end_1
	wflip jmp_resume+w, resume_print_data ^ end_1, digits+dw*0x8

	end_1:
	// print 0x5 (using the digits array) and return to end_cont
	wflip jmp_resume+w, end_1 ^ end_cont, digits+dw*0x5

//////////////////////////////////////////////////
b13xor:
	jmp_data+dbit+8;counter+9*dw
//////////////////////////////////////////////////

b14:
	jmp_data+dbit+9;jmp_loop

//////////////////////////////////////////////////
end_print_code_3:
	// set jmp_data to start over

	// can't use wflip here because it would create a wflip_area in the end
	// wflip jmp_data+w, (data-0x10) ^ data_end, end_print_code_4
	jmp_data+w+4;
	jmp_data+w+5;
	jmp_data+w+11;
	jmp_data+w+14;end_print_code_4
//////////////////////////////////////////////////

// 0x400
//////////////////////////////////////////////////
flip_area:
	counter:
		;((data>> 4)&1) ? b5_alt  : b5
		;((data>> 5)&1) ? b6_alt  : b6
		;((data>> 6)&1) ? b7_alt  : b7
		;((data>> 7)&1) ? b8_alt  : b8
		;((data>> 8)&1) ? b9_alt  : b9
		;((data>> 9)&1) ? b10_alt : b10
		;((data>>10)&1) ? b11_alt : b11
		;((data>>11)&1) ? b12_alt : b12
		;((data>>12)&1) ? b13_alt : b13
		;((data>>13)&1) ? b14_alt : b14

	// bits may have been flipped in this area, so if we know
	// a bit would end up flipped when we reach end_print_code, we need to
	// define it "unflipped" here

end_print_code_4:
	// set resume to resume (will be alternated to resume_print_data)
	// 0xb60	resume_print_data
	// 0xb100	flip_data_bit
	(jmp_resume+w+6)^0x0;

        // reset where "flip_data_bit" jump to
	// 0xc00	inc
	// 0xc20	jmp_data
	(jmp_after_flip+w+5)^0x1;

	// set jmp_loop to skip printing the padding word
	// 0xb100	flip_data_bit
	// 0xb80	loop_print_data
	(jmp_loop+w+5)^0x0;

	// set data_end to jump to end and start loop again
	// 0x300	end
	// 0xb00	end_print_code
	(data_end+w+11)^0x1;jmp_loop

	0;			// USE WITH CARE, MIGHT BE FLIPPED
	0;			// USE WITH CARE, MIGHT BE FLIPPED
//////////////////////////////////////////////////

// 0x600
//////////////////////////////////////////////////
def digit_jmp addr, i {
  dw + (i % 2); addr + ((i>>1) * dw)
}

digits:
rep(16, i) .digit_jmp p000, i

p000:
rep(8, i) .digit_jmp p00, i

p00:
rep(4, i) .digit_jmp p0, i

p0:
dw+0;jmp_resume
dw+1;jmp_resume
//////////////////////////////////////////////////

//////////////////////////////////////////////////
end_print_code_1:
	// 0xc60 - 0x10	(data - 0x10)
	// 0x4460	data_end

	// since the data pointer is pointing to the end (data_end), we need to bring it back
	// to the beginning (data); actually, we bring it one word earlier because we want
	// to print the first word of data (0x0)

	// bits of (data ^ data_end (offset by -4)). Bit 14 shouldn't be flipped
	wflip counter+(4-4)*dw+w, b5 ^ b5_alt, end_print_code_2		// alternate b5 with b5_alt
//////////////////////////////////////////////////

// 0x9E0
print_dwsize_padding:
	// dw+0;	// done before calling this method

	zero_padding=0x0
	// print 0x0 (using the digits array) and return to unflip_jump
	p0+((zero_padding >> 4) & 1)*dw + dbit;digits+dw*zero_padding

	unflip_jump:
	// 0x2C0
	p0+((zero_padding >> 4) & 1)*dw + dbit;flip_data_bit

// 0xA20
jmp_resume:
	// saving an op by flipping counter*0*dw+w bit here before jumping to resume (which would always flip it)

	// alternate b5 with b5_alt
	wflip counter+0*dw+w, b5 ^ b5_alt, flip_data_bit

// 0xA40
print_data_padding:
	// dw+1;	// done before calling this label 

	// ((digits >> 10) & 0xF):
	char2=0x1
	p0+((char2 >> 4) & 1)*dw + dbit + 1;digits+dw*char2

	// 0x320
	dw+((digits >> 14) & 0x1);

	dw+((digits >> 15) & 0x1);
	p0+((char2 >> 4) & 1)*dw + dbit + 1;flip_data_bit

	// ^ the operation above can probably be merged with the last operation
	// in print_dwsize_padding if the flip word be a bit print (dw+0/1) that's used
	// for both print_data_padding and print_dwsize_padding


//////////////////////////////////////////////////
end_print_code_2:
	wflip counter+(5-4)*dw+w, b6 ^ b6_alt
	wflip counter+(11-4)*dw+w, b12 ^ b12_alt, end_print_code_3
//////////////////////////////////////////////////


// 0xB00
// end_print_code is spaghetti code because it's occupying the padding areas that were
// left to align some labels
end_print_code:
	// we need to unflip data_end's data bits since we didn't go to "resume" after this cycle
	data_end+w-7;end_print_code_1

// 0xB20
resume_print_data:
	dw+((digits >> 9) & 0x1);print_data_padding

// 0xB40
loop_print_data:
	dw+0;print_dwsize_padding

// 0xB60
flip_data_bit:
	jmp_data+w+0;
	jmp_data+w+3;

	wflip jmp_after_flip+w, inc ^ jmp_data, jmp_data+w


//////////////////////////////////////////////////
after_flip:
	jmp_data+w+0;

	jmp_after_flip:
	jmp_data+w+3;inc	// <- `inc` here will be alternated with `jmp_data` by flip_data_bit
//////////////////////////////////////////////////


// 0xc00
//////////////////////////////////////////////////
inc:
	// counter+0 has already been flipped by jmp_resume
	jmp_data+dbit-1;counter+0*dw
////////////////////////////////////////////////////

// 0xc20
////////////////////////////////////////////////////
// [jmp_data] will jump to data (flip 0; jump to data)
// [jmp_data+w] will flip data and jump to after_flip, but
// bits 0+3 needs to be set (and then unset) before using it that way
// this is calculated as follow:
// 0x400	flip_area
// 0x600	digits
// [flip_area] ^ [digits] = 0x200, which has the 9th bit set
// 9 is 0b1001, so we need to flip those bits
jmp_data:
	;data+0*w

	after_flip;digits+dw*0x0

// 0xc60
data:
digits+dw*0x0;digits+dw*0x6
digits+dw*0x4;digits+dw*0xa
digits+dw*0x4;digits+dw*0x0
digits+dw*0x1;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x1
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x8
digits+dw*0x4;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x8
digits+dw*0x4;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0xb
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x8
digits+dw*0x3;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x0
digits+dw*0x0;digits+dw*0x6
digits+dw*0x5;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x1
digits+dw*0x0;digits+dw*0x5
digits+dw*0x7;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x1
digits+dw*0x0;digits+dw*0x5
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0xb
digits+dw*0x0;digits+dw*0x6
digits+dw*0x9;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x1
digits+dw*0x0;digits+dw*0x6
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x4
digits+dw*0x0;digits+dw*0x5
digits+dw*0xb;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x2
digits+dw*0x0;digits+dw*0x8
digits+dw*0xd;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x2
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x0
digits+dw*0x0;digits+dw*0x7
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x4
digits+dw*0x0;digits+dw*0x8
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x4
digits+dw*0x0;digits+dw*0x7
digits+dw*0xf;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x2
digits+dw*0x0;digits+dw*0x9
digits+dw*0x1;digits+dw*0x5
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x2
digits+dw*0x0;digits+dw*0x9
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x2
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x2
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x2
digits+dw*0x0;digits+dw*0xa
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x4
digits+dw*0x0;digits+dw*0xb
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x4
digits+dw*0x0;digits+dw*0x9
digits+dw*0x3;digits+dw*0x5
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x3
digits+dw*0x0;digits+dw*0xc
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x5
digits+dw*0x0;digits+dw*0xb
digits+dw*0x3;digits+dw*0xa
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x7
digits+dw*0x0;digits+dw*0x8
digits+dw*0x3;digits+dw*0xa
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x6
digits+dw*0x0;digits+dw*0xd
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x5
digits+dw*0x0;digits+dw*0xe
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x0
digits+dw*0x0;digits+dw*0x4
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x3
digits+dw*0x0;digits+dw*0x5
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x3
digits+dw*0x0;digits+dw*0xb
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x3
digits+dw*0x0;digits+dw*0xe
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x5
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x1
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x1
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x1
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x1
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x2
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x3
digits+dw*0x0;digits+dw*0x6
digits+dw*0x3;digits+dw*0xa
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x5
digits+dw*0x0;digits+dw*0x4
digits+dw*0xf;digits+dw*0xb
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x5
digits+dw*0x0;digits+dw*0x5
digits+dw*0xd;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x5
digits+dw*0x0;digits+dw*0xa
digits+dw*0x7;digits+dw*0x4
digits+dw*0x4;digits+dw*0x0
digits+dw*0xc;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x5
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x6
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x8
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x8
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0xa
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0xa
digits+dw*0x0;digits+dw*0x7
digits+dw*0x1;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0xa
digits+dw*0x0;digits+dw*0x5
digits+dw*0x9;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x6
digits+dw*0x0;digits+dw*0x5
digits+dw*0x9;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0xb
digits+dw*0x0;digits+dw*0x7
digits+dw*0x1;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0xb
digits+dw*0x0;digits+dw*0x6
digits+dw*0x9;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x6
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0xa
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0xa
digits+dw*0x0;digits+dw*0x6
digits+dw*0x9;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0xb
digits+dw*0x0;digits+dw*0x8
digits+dw*0x3;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0xa
digits+dw*0x0;digits+dw*0x7
digits+dw*0xf;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0x3
digits+dw*0x0;digits+dw*0x9
digits+dw*0x6;digits+dw*0x4
digits+dw*0x4;digits+dw*0x0
digits+dw*0xc;digits+dw*0x9
digits+dw*0x0;digits+dw*0x1
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x4;digits+dw*0xa
digits+dw*0x0;digits+dw*0x0
digits+dw*0x2;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0x9
digits+dw*0x0;digits+dw*0x0
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x8;digits+dw*0xb
digits+dw*0x0;digits+dw*0x3
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xa;digits+dw*0xb
digits+dw*0x0;digits+dw*0x5
digits+dw*0xf;digits+dw*0xb
digits+dw*0x0;digits+dw*0x0
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xe;digits+dw*0xb
digits+dw*0x0;digits+dw*0x3
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0xc
digits+dw*0x0;digits+dw*0x4
digits+dw*0x3;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x4
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x0
digits+dw*0x6;digits+dw*0xc
digits+dw*0x0;digits+dw*0x0
digits+dw*0xc;digits+dw*0xb
digits+dw*0x0;digits+dw*0x0
digits+dw*0x0;digits+dw*0x6
data_end:
digits+dw*0x0;end_print_code