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 long long MOD = 1e9 + 7, base = 233, invb = 90128756;
char s[2][2005], t[2005];
int n, m;
long long val[2][2005], v1[2005], v2[2005], f[2005][2005][2], pwb[2005],
    pwi[2005], ans;
void solve() {
  for (int i = 1; i <= n; i++) {
    val[0][i] = (val[0][i - 1] * base + s[0][i]) % MOD;
    val[1][i] = (val[1][i - 1] * base + s[1][i]) % MOD;
  }
  memset(f, 0, sizeof(f));
  for (int i = 1; i <= n; i++) {
    for (int len = 2; len < i && 2 * len <= m; len++) {
      long long v11 =
          (val[0][i - 1] - val[0][i - len - 1] * pwb[len] % MOD + MOD) % MOD;
      long long v12 =
          (val[1][i - 1] - val[1][i - len - 1] * pwb[len] % MOD + MOD) % MOD;
      long long v21 = (v1[2 * len] - v1[len] * pwb[len] % MOD + MOD) % MOD;
      long long v22 = (v2[1] - v2[len + 1] * pwb[len] % MOD + MOD) % MOD;
      if (v11 == v22 && v12 == v21) f[i][2 * len + 1][1]++;
      if (v11 == v21 && v12 == v22) f[i][2 * len + 1][0]++;
    }
    for (int j = 1; j <= m + 1; j++)
      for (int d = 0; d < 2; d++) {
        f[i][1][d]++;
        if (j <= m && t[j] != s[d][i]) {
          f[i][j][d] = 0;
          continue;
        }
        f[i][j][d] %= MOD;
        if (j < m) f[i + 1][j + 1][d] += f[i][j][d];
        if (j < m - 1 && s[d ^ 1][i] == t[j + 1])
          f[i + 1][j + 2][d ^ 1] += f[i][j][d];
        if ((m - j) % 2 == 1) {
          int len = (m - j + 1) / 2;
          if (i + len - 1 > n) continue;
          long long val1 =
              (val[d][i + len - 1] - val[d][i - 1] * pwb[len] % MOD + MOD) %
              MOD;
          long long val2 = (val[d ^ 1][i + len - 1] -
                            val[d ^ 1][i - 1] * pwb[len] % MOD + MOD) %
                           MOD;
          if (val1 ==
                  (v1[j + len - 1] - v1[j - 1] * pwb[len] % MOD + MOD) % MOD &&
              val2 == v2[j + len])
            ans += f[i][j][d];
        }
      }
    ans += f[i][m][0] + f[i][m][1];
  }
}
int main() {
  scanf("%s%s%s", s[0] + 1, s[1] + 1, t + 1);
  n = (int)strlen(s[0] + 1);
  m = (int)strlen(t + 1);
  if (m == 1) {
    for (int i = 1; i <= n; i++) {
      if (s[0][i] == t[1]) ans++;
      if (s[1][i] == t[1]) ans++;
    }
    printf("%lld\n", ans);
    return 0;
  }
  for (int i = 1; i <= m; i++) v1[i] = (v1[i - 1] * base + t[i]) % MOD;
  for (int i = m; i >= 1; i--) v2[i] = (v2[i + 1] * base + t[i]) % MOD;
  pwb[0] = pwi[0] = 1;
  for (int i = 1; i <= max(n, m); i++) {
    pwb[i] = pwb[i - 1] * base % MOD;
    pwi[i] = pwi[i - 1] * invb % MOD;
  }
  solve();
  for (int i = 1; i * 2 <= n; i++) {
    swap(s[0][i], s[0][n - i + 1]);
    swap(s[1][i], s[1][n - i + 1]);
  }
  solve();
  if (m == 2) {
    for (int i = 1; i <= n; i++) {
      if (s[0][i] == t[1] && s[1][i] == t[2]) ans--;
      if (s[0][i] == t[2] && s[1][i] == t[1]) ans--;
    }
  }
  printf("%lld\n", ans % MOD);
  return 0;
}