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 _ = 2003, P = 1e9 + 7;
void inc(int &a, int b) { a = a + b >= P ? a + b - P : a + b; }
char str[2][_], mod[_];
int tol[2][_][_], tor[2][_][_], dpl[2][_][_], dpr[2][_][_], N, K;
int main() {
  scanf("%s %s", str[0] + 1, str[1] + 1);
  N = strlen(str[0] + 1);
  scanf("%s", mod + 1);
  K = strlen(mod + 1);
  for (int i = 0; i < 2; ++i)
    for (int j = 1; j <= N; ++j) tol[i][j][K + 1] = tor[i][j][K + 1] = K + 1;
  for (int i = 0; i < 2; ++i)
    for (int j = 0; j <= K + 1; ++j) tol[i][0][j] = tor[i][N + 1][j] = j;
  for (int L = K; L; --L)
    for (int i = 0; i < 2; ++i)
      for (int j = 1; j <= N; ++j)
        if (mod[L] == str[i][j]) {
          tol[i][j][L] = tol[i][j - 1][L + 1];
          tor[i][j][L] = tor[i][j + 1][L + 1];
        } else
          tol[i][j][L] = tor[i][j][L] = L;
  for (int L = K; L; --L)
    for (int i = 0; i < 2; ++i)
      for (int j = 1; j <= N; ++j)
        if (tol[i][j][L] != L)
          if (L == K)
            dpl[i][j][L] = dpr[i][j][L] = 1;
          else {
            inc(dpl[i][j][L], dpl[i][j - 1][L + 1]);
            inc(dpr[i][j][L], dpr[i][j + 1][L + 1]);
            if (str[i ^ 1][j] == mod[L + 1] && L != K - 1) {
              inc(dpl[i][j][L], dpl[i ^ 1][j - 1][L + 2]);
              inc(dpr[i][j][L], dpr[i ^ 1][j + 1][L + 2]);
            }
            int len = (K + 1 - L) / 2;
            if (!((K + 1 - L) & 1)) {
              dpl[i][j][L] += tol[i][j][L] >= L + len &&
                              tor[i ^ 1][j - len + 1][L + len] == K + 1;
              dpr[i][j][L] += tor[i][j][L] >= L + len &&
                              tol[i ^ 1][j + len - 1][L + len] == K + 1;
            }
          }
  int sum = 0;
  for (int i = 0; i < 2; ++i)
    for (int j = 1; j <= N; ++j) {
      for (int k = 1; k < tol[i][j][1]; ++k) {
        if (tor[i ^ 1][j - k + 1][k + 1] >= min(K + 1, 2 * k + 1))
          if (2 * k + 1 < K + 1)
            inc(sum, dpr[i ^ 1][j + 1][2 * k + 1]);
          else
            ++sum;
        if (k != 1 && k < K - 1 && tol[i ^ 1][j - k + 1][k + 1] != k + 1)
          inc(sum, dpl[i ^ 1][j - k][k + 2]);
      }
      for (int k = 1; k < tor[i][j][1]; ++k) {
        if (tol[i ^ 1][j + k - 1][k + 1] >= min(K + 1, 2 * k + 1))
          if (2 * k + 1 < K + 1)
            inc(sum, dpl[i ^ 1][j - 1][2 * k + 1]);
          else
            sum += k != 1;
        if (k != 1 && k < K - 1 && tor[i ^ 1][j + k - 1][k + 1] != k + 1)
          inc(sum, dpr[i ^ 1][j + k][k + 2]);
      }
    }
  cout << (sum % P + P) % P;
  return 0;
}