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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 $$$r_0$$$ and all ones in $$$s$$$ with some other string $$$r_1$$$ and obtain $$$t$$$. The strings $$$r_0$$$ and $$$r_1$$$ 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 $$$r_0$$$ and $$$r_1$$$) that transform $$$s$$$ to $$$t$$$.

Input

The first line contains a string $$$s$$$ ($$$2 \le |s| \le 10^5$$$) consisting of zeros and ones — the original signal.

The second line contains a string $$$t$$$ ($$$1 \le |t| \le 10^6$$$) 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 $$$r_0$$$ and $$$r_1$$$ 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 $$$(r_0, r_1)$$$ are as follows:

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

The pair "aaa", "aaa" is not allowed, since $$$r_0$$$ and $$$r_1$$$ must be different.

In the second example, the following pairs are possible:

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