#include <bits/stdc++.h>
using namespace std;
const int inf = 1e9;
const long long Inf = 1e18;
const int N = 1e6 + 10;
const int mod = 998244853;
const unsigned long long base = 131;
int gi() {
  int x = 0, o = 1;
  char ch = getchar();
  while ((ch < '0' || ch > '9') && ch != '-') ch = getchar();
  if (ch == '-') o = -1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return x * o;
}
template <typename T>
bool chkmax(T &a, T b) {
  return a < b ? a = b, 1 : 0;
};
template <typename T>
bool chkmin(T &a, T b) {
  return a > b ? a = b, 1 : 0;
};
int add(int a, int b) { return a + b >= mod ? a + b - mod : a + b; }
int sub(int a, int b) { return a - b < 0 ? a - b + mod : a - b; }
void inc(int &a, int b) { a = (a + b >= mod ? a + b - mod : a + b); }
void dec(int &a, int b) { a = (a - b < 0 ? a - b + mod : a - b); }
char s[N], t[N];
int n, m, a = 0, b = 0, hsh[N], pw[N];
unsigned long long gethsh(int l, int r) {
  return sub(hsh[r], 1ll * hsh[l - 1] * pw[r - l + 1] % mod);
}
int check(int len0) {
  int len1 = (m - a * len0) / b;
  int v0 = 0, v1 = 0;
  unsigned long long h0 = 0, h1 = 0;
  for (int i = 1, j = 1; i <= n; i++) {
    if (s[i] == '0') {
      if (!v0)
        h0 = gethsh(j, j + len0 - 1), v0 = 1;
      else if (gethsh(j, j + len0 - 1) != h0)
        return 0;
      j += len0;
    } else {
      if (!v1)
        h1 = gethsh(j, j + len1 - 1), v1 = 1;
      else if (gethsh(j, j + len1 - 1) != h1)
        return 0;
      j += len1;
    }
  }
  if (h0 == h1) return 0;
  return 1;
}
int main() {
  scanf("%s", s + 1), n = strlen(s + 1);
  scanf("%s", t + 1), m = strlen(t + 1);
  for (int i = 1; i <= n; i++)
    if (s[i] == '0')
      ++a;
    else
      ++b;
  int ans = 0;
  pw[0] = 1;
  for (int i = 1; i <= m; i++) pw[i] = 1ll * pw[i - 1] * base % mod;
  for (int i = 1; i <= m; i++)
    hsh[i] = add(1ll * hsh[i - 1] * base % mod, t[i] - 'a' + 1);
  for (int i = 1; i <= m; i++)
    if (1ll * a * i <= m && (m - a * i) % b == 0 && (m - a * i) / b > 0 &&
        check(i))
      ++ans;
  printf("%d\n", ans);
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 ≤ |s| ≤ 10^5) consisting of zeros and ones — the original signal.

The second line contains a string t (1 ≤ |t| ≤ 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" 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int inf = 1e9;
const long long Inf = 1e18;
const int N = 1e6 + 10;
const int mod = 998244853;
const unsigned long long base = 131;
int gi() {
  int x = 0, o = 1;
  char ch = getchar();
  while ((ch < '0' || ch > '9') && ch != '-') ch = getchar();
  if (ch == '-') o = -1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return x * o;
}
template <typename T>
bool chkmax(T &a, T b) {
  return a < b ? a = b, 1 : 0;
};
template <typename T>
bool chkmin(T &a, T b) {
  return a > b ? a = b, 1 : 0;
};
int add(int a, int b) { return a + b >= mod ? a + b - mod : a + b; }
int sub(int a, int b) { return a - b < 0 ? a - b + mod : a - b; }
void inc(int &a, int b) { a = (a + b >= mod ? a + b - mod : a + b); }
void dec(int &a, int b) { a = (a - b < 0 ? a - b + mod : a - b); }
char s[N], t[N];
int n, m, a = 0, b = 0, hsh[N], pw[N];
unsigned long long gethsh(int l, int r) {
  return sub(hsh[r], 1ll * hsh[l - 1] * pw[r - l + 1] % mod);
}
int check(int len0) {
  int len1 = (m - a * len0) / b;
  int v0 = 0, v1 = 0;
  unsigned long long h0 = 0, h1 = 0;
  for (int i = 1, j = 1; i <= n; i++) {
    if (s[i] == '0') {
      if (!v0)
        h0 = gethsh(j, j + len0 - 1), v0 = 1;
      else if (gethsh(j, j + len0 - 1) != h0)
        return 0;
      j += len0;
    } else {
      if (!v1)
        h1 = gethsh(j, j + len1 - 1), v1 = 1;
      else if (gethsh(j, j + len1 - 1) != h1)
        return 0;
      j += len1;
    }
  }
  if (h0 == h1) return 0;
  return 1;
}
int main() {
  scanf("%s", s + 1), n = strlen(s + 1);
  scanf("%s", t + 1), m = strlen(t + 1);
  for (int i = 1; i <= n; i++)
    if (s[i] == '0')
      ++a;
    else
      ++b;
  int ans = 0;
  pw[0] = 1;
  for (int i = 1; i <= m; i++) pw[i] = 1ll * pw[i - 1] * base % mod;
  for (int i = 1; i <= m; i++)
    hsh[i] = add(1ll * hsh[i - 1] * base % mod, t[i] - 'a' + 1);
  for (int i = 1; i <= m; i++)
    if (1ll * a * i <= m && (m - a * i) % b == 0 && (m - a * i) / b > 0 &&
        check(i))
      ++ans;
  printf("%d\n", ans);
  return 0;
}

```