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E. Check Transcription
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

One of Arkady's friends works at a huge radio telescope. A few decades ago the telescope has sent a signal s towards a faraway galaxy. Recently they've received a response t which they believe to be a response from aliens! The scientists now want to check if the signal t is similar to s.

The original signal s was a sequence of zeros and ones (everyone knows that binary code is the universe-wide language). The returned signal t, however, does not look as easy as s, but the scientists don't give up! They represented t as a sequence of English letters and say that t is similar to s if you can replace all zeros in s with some string r0 and all ones in s with some other string r1 and obtain t. The strings r0 and r1 must be different and non-empty.

Please help Arkady's friend and find the number of possible replacements for zeros and ones (the number of pairs of strings r0 and r1) that transform s to t.

Input

The first line contains a string s (2|s|105) consisting of zeros and ones — the original signal.

The second line contains a string t (1|t|106) consisting of lowercase English letters only — the received signal.

It is guaranteed, that the string s contains at least one '0' and at least one '1'.

Output

Print a single integer — the number of pairs of strings r0 and r1 that transform s to t.

In case there are no such pairs, print 0.

Examples
Input
01
aaaaaa
Output
4
Input
001
kokokokotlin
Output
2
Note

In the first example, the possible pairs (r0,r1) are as follows:

  • "a", "aaaaa"
  • "aa", "aaaa"
  • "aaaa", "aa"
  • "aaaaa", "a"

The pair "aaa", "aaa" is not allowed, since r0 and r1 must be different.

In the second example, the following pairs are possible:

  • "ko", "kokotlin"
  • "koko", "tlin"