CF182D.Common Divisors

Vasya has recently learned at school what a number's divisor is and decided to determine a string's divisor. Here is what he came up with.

String a is the divisor of string b if and only if there exists a positive integer x such that if we write out string a consecutively x times, we get string b. For example, string "abab" has two divisors — "ab" and "abab".

Now Vasya wants to write a program that calculates the number of common divisors of two strings. Please help him.

瓦西娅最近在学校学习了数的约数概念，并决定将这一概念推广到字符串上，定义字符串的“约数”。他的定义如下：

字符串 $a$ 是字符串 $b$ 的约数，当且仅当存在某个正整数 $x$，使得将字符串 $a$ 连续重复 $x$ 次后，恰好得到字符串 $b$。例如，字符串 "abab" 有两个约数："ab" 和 "abab"。

现在，瓦西娅想编写一个程序，用于计算两个字符串的公共约数的个数。请帮助他完成这一任务。

The first input line contains a non-empty string _s_1.

The second input line contains a non-empty string _s_2.

Lengths of strings _s_1 and _s_2 are positive and do not exceed 105. The strings only consist of lowercase Latin letters.

第一行输入包含一个非空字符串 $s_1$。
第二行输入包含一个非空字符串 $s_2$。
字符串 $s_1$ 和 $s_2$ 的长度均为正整数，且不超过 $10^5$。这两个字符串仅由小写拉丁字母组成。

Print the number of common divisors of strings _s_1 and _s_2.

输出字符串 $s_1$ 和 $s_2$ 的公共因子的数量。

In first sample the common divisors are strings "abcd" and "abcdabcd".

In the second sample the common divisor is a single string "a". String "aa" isn't included in the answer as it isn't a divisor of string "aaa".

在第一个样例中，公共因子字符串为 “abcd” 和 “abcdabcd”。

在第二个样例中，公共因子字符串仅有一个：“a”。字符串 “aa” 不在答案中，因为它不是字符串 “aaa” 的因子。