Given strings s1, s2, and s3, find whether s3 is formed by an interleaving of s1 and s2.

An interleaving of two strings s and t is a configuration where s and t are divided into n and m substrings respectively, such that:

• s = s1 + s2 + ... + sn
• t = t1 + t2 + ... + tm
• |n - m| <= 1
• The interleaving is s1 + t1 + s2 + t2 + s3 + t3 + ... or t1 + s1 + t2 + s2 + t3 + s3 + ...

Note: a + b is the concatenation of strings a and b.

Examples

Example 1

Input:  s1 = "aabcc", s2 = "dbbca", s3 = "aadbbcbcac"
Output: true

Example 2

Input:  s1 = "aabcc", s2 = "dbbca", s3 = "aadbbbaccc"
Output: false

Example 3

Input:  s1 = "", s2 = "", s3 = ""
Output: true

Constraints

• 0 <= s1.length, s2.length <= 100
• 0 <= s3.length <= 200
• s1, s2, and s3 consist of lowercase English letters