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;
char ch[3][2005], t[2005];
long long Hase1[3][2005], Hase2[3][2005], Hasht[2005], pow1[2005];
long long n, m, f[3][2005][2005], g[3][2005][2005], ans, gs;
inline long long get1(long long l, long long r, long long id) {
  return Hase1[id][r] - Hase1[id][l - 1] * pow1[r - l + 1];
}
inline long long get2(long long l, long long r, long long id) {
  return Hase2[id][l] - Hase2[id][r + 1] * pow1[r - l + 1];
}
inline long long merge(long long H1, long long H2, long long len) {
  return H2 + H1 * pow1[len];
}
inline void dp() {
  memset(f, 0, sizeof(f));
  memset(g, 0, sizeof(g));
  for (long long i = 1; i <= m; i++)
    Hasht[i] = Hasht[i - 1] * 131 + (t[i] - 'a' + 1);
  for (long long i = 1; i <= 2; i++)
    for (long long j = 1; j <= n; j++)
      for (long long k = j; k >= 1; k--) {
        long long len = 2 * (j - k + 1);
        if (len > m) continue;
        long long HA = get1(k, j, i);
        long long HB = get2(k, j, 3 - i);
        long long HH = Hasht[len];
        if (merge(HB, HA, j - k + 1) == HH) {
          if (len == m)
            gs++;
          else
            g[i][j][len] = 1;
        }
      }
  for (long long i = 1; i <= 2; i++)
    for (long long j = 1; j <= n; j++)
      if (ch[i][j] == t[1]) g[i][j][1] = 1;
  for (long long i = m; i >= 1; i--)
    Hasht[i] = Hasht[i + 1] * 131 + (t[i] - 'a' + 1);
  for (long long k = 1; k < m; k++)
    for (long long j = 1; j <= n; j++)
      for (long long i = 1; i <= 2; i++) {
        if (g[i][j][k])
          if (j < n && ch[i][j + 1] == t[k + 1])
            f[i][j + 1][k + 1] = (f[i][j + 1][k + 1] + g[i][j][k]) % 1000000007;
        if (f[i][j][k]) {
          if (j < n && ch[i][j + 1] == t[k + 1])
            f[i][j + 1][k + 1] = (f[i][j][k] + f[i][j + 1][k + 1]) % 1000000007;
          if (ch[3 - i][j] == t[k + 1])
            g[3 - i][j][k + 1] = (g[3 - i][j][k + 1] + f[i][j][k]) % 1000000007;
        }
      }
  for (long long i = 1; i <= 2; i++)
    for (long long j = 1; j <= n; j++) {
      if (ch[i][j] == t[m]) {
        if (m == 1) ans = (ans + 1) % 1000000007;
        ans = (ans + f[i][j - 1][m - 1]) % 1000000007;
        ans = (ans + g[i][j - 1][m - 1]) % 1000000007;
      }
      for (long long k = j; k <= n; k++) {
        long long len = (k - j + 1) * 2;
        if (len > m) continue;
        long long HA = get1(j, k, 3 - i);
        long long HB = get2(j, k, i);
        long long HH = Hasht[m - len + 1];
        if (merge(HA, HB, k - j + 1) == HH) {
          if (len == m && m != 2)
            gs++;
          else {
            ans = ((ans + f[i][j - 1][m - len]) % 1000000007 +
                   g[i][j - 1][m - len]) %
                  1000000007;
          }
        }
      }
    }
}
signed main() {
  scanf("%s", ch[1] + 1);
  scanf("%s", ch[2] + 1);
  n = strlen(ch[1] + 1);
  scanf("%s", t + 1);
  m = strlen(t + 1);
  pow1[0] = 1;
  for (long long i = 1; i <= max(n, m); i++) pow1[i] = pow1[i - 1] * 131;
  for (long long i = 1; i <= 2; i++)
    for (long long j = 1; j <= n; j++)
      Hase1[i][j] = Hase1[i][j - 1] * 131 + (ch[i][j] - 'a' + 1);
  for (long long i = 1; i <= 2; i++)
    for (long long j = n; j >= 1; j--)
      Hase2[i][j] = Hase2[i][j + 1] * 131 + (ch[i][j] - 'a' + 1);
  dp();
  reverse(t + 1, t + 1 + m);
  dp();
  ans = (ans + gs / 2) % 1000000007;
  if (m == 1) ans /= 2;
  cout << ans;
}