Regular Expression Matching

Given an input string s and a pattern p, implement regular expression matching with support for . and *.

The matching should cover the entire input string (not partial).

Note

s could be empty and contains only lowercase letters a-z.
p could be empty and contains only lowercase letters a-z, and characters like . or *.

Examples

Example #1

Input:

s = 'aa'
p = 'a'

Output: false

Explanation: a does not match the entire string aa.

Example #2

Input:

s = 'aa'
p = 'a*'

Output: true

Explanation: * means zero or more of the preceding element, a. Therefore, by repeating a once, it becomes aa.

Example #3

Input:

s = 'ab'
p = '.*'

Output: true

Explanation: .* means "zero or more (*) of any character (.)".

Example #4

Input:

s = 'aab'
p = 'c*a*b'

Output: true

Explanation: c can be repeated 0 times, a can be repeated 1 time. Therefore it matches aab.