CF1056E.Check Transcription

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 $t$.

Arkady 的一位朋友在一座大型射电望远镜工作。几十年前，该望远镜曾向遥远的星系发送了一个信号 $s$。最近，他们接收到了一个回复信号 $t$，并认为这很可能是外星文明的回应！科学家们现在希望检验信号 $t$ 是否与 $s$ 相似。

原始信号 $s$ 是一个由 0 和 1 组成的序列（众所周知，二进制编码是宇宙通用的语言）。然而，接收到的信号 $t$ 却并不像 $s$ 那样简单，但科学家们并未放弃！他们将 $t$ 表示为一串英文字母，并称：若能将 $s$ 中的所有 0 替换为某个字符串 $r_0$、所有 1 替换为另一个字符串 $r_1$ 后恰好得到 $t$，则称 $t$ 与 $s$ 相似。其中，字符串 $r_0$ 和 $r_1$ 必须互不相同且均非空。

请帮助 Arkady 的这位朋友，计算出所有可能的 $(r_0, r_1)$ 替换对的数量（即满足将 $s$ 变换为 $t$ 的非空且互异的字符串对 $r_0$、$r_1$ 的个数）。

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'.

第一行包含一个由 0 和 1 组成的字符串 $s$（$2 \le |s| \le 10^5$）——原始信号。

第二行包含一个仅由小写英文字母组成的字符串 $t$（$1 \le |t| \le 10^6$）——接收到的信号。

保证字符串 $s$ 中至少包含一个 '0' 和一个 '1'。

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 $0$.

输出一个整数——能够将字符串 $s$ 变换为字符串 $t$ 的字符串对 $r_0$ 和 $r_1$ 的数量。

若不存在这样的字符串对，则输出 $0$。

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"

在第一个例子中，可能的数对 $(r_0, r_1)$ 如下：

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

数对 "aaa", "aaa" 是不允许的，因为 $r_0$ 和 $r_1$ 必须不同。

在第二个例子中，以下数对是可能的：

• "ko", "kokotlin"
• "koko", "tlin"