Reference: Codeforces 182D — Common Divisors

A string ~a~ is called a divisor of a string ~b~ if there exists a positive integer ~x~ such that writing ~a~ exactly ~x~ consecutive times produces ~b~.

For example, the string abab has two divisors:

ab abab

You are given two non-empty strings ~s_1~ and ~s_2~.

Find the number of strings that are divisors of both ~s_1~ and ~s_2~.

Input

• The first line contains the string ~s_1~.
• The second line contains the string ~s_2~.

Output

• Print the number of common divisors of the two strings.

Constraints

• ~1 \le |s_1|, |s_2| \le 10^5~
• Both strings contain only lowercase English letters.

Example 1

Input:

abcdabcd
abcdabcdabcdabcd

Output:

2