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

• '.' Matches any single character.
• '*' Matches zero or more of the preceding element.

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

Examples

Example 1

Input:  s = "aa", p = "a"
Output: false

"a" does not match the entire string "aa".

Example 2

Input:  s = "aa", p = "a*"
Output: true

'*' 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

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

Constraints

• 1 <= s.length <= 20
• 1 <= p.length <= 20
• s contains only lowercase English letters.
• p contains only lowercase English letters, '.', and '*'.
• It is guaranteed for each appearance of the character '*', there will be a previous valid character to match.