Problem: Oleg Petrov loves crossword puzzles and every Thursday he buys his favorite magazine with crosswords and other word puzzles. In the last magazine Oleg found a curious puzzle, and the magazine promised a valuable prize for it's solution. We give a formal description of the problem below.

The puzzle field consists of two rows, each row contains n cells. Each cell contains exactly one small English letter. You also are given a word w, which consists of k small English letters. A solution of the puzzle is a sequence of field cells c1, ..., ck, such that:

  * For all i from 1 to k the letter written in the cell ci matches the letter wi;
  * All the cells in the sequence are pairwise distinct;
  * For all i from 1 to k - 1 cells ci and ci + 1 have a common side.



Oleg Petrov quickly found a solution for the puzzle. Now he wonders, how many distinct solutions are there for this puzzle. Oleg Petrov doesn't like too large numbers, so calculate the answer modulo 109 + 7.

Two solutions ci and c'i are considered distinct if the sequences of cells do not match in at least one position, that is there is such j in range from 1 to k, such that cj ≠ c'j.

Input

The first two lines contain the state of the field for the puzzle. Each of these non-empty lines contains exactly n small English letters.

The next line is left empty.

The next line is non-empty and contains word w, consisting of small English letters.

The length of each line doesn't exceed 2 000.

Output

Print a single integer — the number of distinct solutions for the puzzle modulo 109 + 7.

Examples

Input

code
edoc

code


Output

4


Input

aaa
aaa

aa


Output

14

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int Maxn = 2005, p = 1e9 + 7;
int n, m, lcs[2][2][Maxn][Maxn], lcp[2][2][Maxn][Maxn], f[2][Maxn][Maxn],
    g[2][Maxn][Maxn];
bool mat[2][2][Maxn][Maxn];
long long ans;
char str[2][Maxn], T[Maxn];
void work(void) {
  for (int i = 1; i <= m; i++)
    for (int j = 0; j <= 1; j++) {
      for (int k = 1; k <= n; k++)
        lcs[0][j][k][i] = (str[j][k] == T[i]) ? lcs[0][j][k - 1][i - 1] + 1 : 0;
      for (int k = n; k >= 1; k--)
        lcs[1][j][k][i] = (str[j][k] == T[i]) ? lcs[1][j][k + 1][i - 1] + 1 : 0;
    }
  for (int i = m; i >= 1; i--)
    for (int j = 0; j <= 1; j++) {
      for (int k = 1; k <= n; k++)
        lcp[0][j][k][i] = (str[j][k] == T[i]) ? lcp[0][j][k - 1][i + 1] + 1 : 0;
      for (int k = n; k >= 1; k--)
        lcp[1][j][k][i] = (str[j][k] == T[i]) ? lcp[1][j][k + 1][i + 1] + 1 : 0;
    }
  for (int i = 0; i <= 1; i++)
    for (int j = 1; j <= n; j++) {
      for (int k = 2; k <= min(j, m / 2); k++)
        mat[0][i][j][k] =
            lcp[0][i ^ 1][j][1] >= k && lcp[1][i][j - k + 1][k + 1] >= k;
      for (int k = 2; k <= min(n - j + 1, m / 2); k++)
        mat[1][i][j][k] =
            lcs[1][i ^ 1][j][m] >= k && lcs[0][i][j + k - 1][m - k] >= k;
    }
  if (m % 2 == 0) {
    for (int j = 1; j <= n; j++)
      ans += (int)mat[0][1][j][m / 2] + mat[1][1][j][m / 2];
    for (int i = 0; i <= 1; i++)
      for (int j = 1; j <= n; j++)
        for (int k = 2; k <= m / 2 - 2; k++)
          ans += (mat[0][i][j][k] & mat[1][i][j + 1][m / 2 - k]);
  }
  for (int j = 1; j <= n; j++) {
    for (int i = 0; i <= 1; i++) {
      if (str[i][j] == T[1]) f[i][j][1]++;
      for (int k = 2; k <= m / 2; k++)
        if (mat[0][i][j - 1][k] && str[i][j] == T[2 * k + 1])
          f[i][j][2 * k + 1]++;
      for (int k = 1; k < m; k++)
        if (str[i][j] == T[k + 1])
          f[i][j][k + 1] =
              ((long long)f[i][j][k + 1] + f[i][j - 1][k] + g[i][j - 1][k]) % p;
      for (int k = 1; k < m; k++)
        if (str[i ^ 1][j] == T[k + 1]) (g[i ^ 1][j][k + 1] += f[i][j][k]) %= p;
    }
    for (int i = 0; i <= 1; i++) {
      (ans += f[i][j][m] + g[i][j][m]) %= p;
      for (int k = 2; k <= m / 2; k++)
        if (mat[1][i][j + 1][k])
          (ans += f[i][j][m - 2 * k] + g[i][j][m - 2 * k]) %= p;
    }
  }
}
void dfs(int x, int y, int d) {
  if (str[x][y] != T[d]) return;
  if (d == m) {
    ans++;
    return;
  }
  if (x == 1)
    dfs(0, y, d + 1);
  else
    dfs(1, y, d + 1);
  if (y != 1) dfs(x, y - 1, d + 1);
  if (y != n) dfs(x, y + 1, d + 1);
}
int main() {
  scanf("%s%s%s", str[0] + 1, str[1] + 1, T + 1);
  n = strlen(str[0] + 1), m = strlen(T + 1);
  if (m <= 2) {
    for (int i = 0; i <= 1; i++)
      for (int j = 1; j <= n; j++) dfs(i, j, 1);
  } else {
    work();
    reverse(T + 1, T + 1 + m);
    memset(f, 0, sizeof(f)), memset(g, 0, sizeof(g));
    work();
  }
  printf("%lld", ans);
  return 0;
}