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;
const int MAXM = 1e5 + 5;
const int P = 1e9 + 7;
template <typename T>
void chkmax(T &x, T y) {
  x = max(x, y);
}
template <typename T>
void chkmin(T &x, T y) {
  x = min(x, y);
}
template <typename T>
void read(T &x) {
  x = 0;
  int f = 1;
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -f;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
  x *= f;
}
namespace SuffixArray {
const int MAXN = 100005;
const int MAXLOG = 20;
const int MAXC = 256;
int sa[MAXN], rnk[MAXN], height[MAXN];
int Min[MAXN][MAXLOG], bit[MAXN], N;
void init(char *a, int n) {
  N = n;
  static int x[MAXN], y[MAXN], cnt[MAXN], rk[MAXN];
  memset(cnt, 0, sizeof(cnt));
  for (int i = 1; i <= n; i++) cnt[(int)a[i]]++;
  for (int i = 1; i <= MAXC; i++) cnt[i] += cnt[i - 1];
  for (int i = n; i >= 1; i--) sa[cnt[(int)a[i]]--] = i;
  rnk[sa[1]] = 1;
  for (int i = 2; i <= n; i++)
    rnk[sa[i]] = rnk[sa[i - 1]] + (a[sa[i]] != a[sa[i - 1]]);
  for (int k = 1; rnk[sa[n]] != n; k <<= 1) {
    for (int i = 1; i <= n; i++) {
      x[i] = rnk[i];
      y[i] = (i + k <= n) ? rnk[i + k] : 0;
    }
    memset(cnt, 0, sizeof(cnt));
    for (int i = 1; i <= n; i++) cnt[y[i]]++;
    for (int i = 1; i <= n; i++) cnt[i] += cnt[i - 1];
    for (int i = n; i >= 1; i--) rk[cnt[y[i]]--] = i;
    memset(cnt, 0, sizeof(cnt));
    for (int i = 1; i <= n; i++) cnt[x[i]]++;
    for (int i = 1; i <= n; i++) cnt[i] += cnt[i - 1];
    for (int i = n; i >= 1; i--) sa[cnt[x[rk[i]]]--] = rk[i];
    rnk[sa[1]] = 1;
    for (int i = 2; i <= n; i++)
      rnk[sa[i]] = rnk[sa[i - 1]] +
                   (x[sa[i]] != x[sa[i - 1]] || y[sa[i]] != y[sa[i - 1]]);
  }
  int now = 0;
  for (int i = 1; i <= n; i++) {
    if (now) now--;
    while (a[i + now] == a[sa[rnk[i] + 1] + now]) now++;
    height[rnk[i]] = now;
  }
  for (int i = 1; i <= n; i++) Min[i][0] = height[i];
  for (int p = 1; p < MAXLOG; p++) {
    int tmp = 1 << (p - 1);
    for (int i = 1, j = tmp + 1; j <= n; i++, j++)
      Min[i][p] = min(Min[i][p - 1], Min[i + tmp][p - 1]);
  }
  for (int i = 1; i <= n; i++) {
    bit[i] = bit[i - 1];
    if (i >= 1 << (bit[i] + 1)) bit[i]++;
  }
}
int lcp(int x, int y) {
  if (x == y) return N - x + 1;
  x = rnk[x], y = rnk[y];
  if (x > y) swap(x, y);
  int tmp = bit[y - x];
  return min(Min[x][tmp], Min[y - (1 << tmp)][tmp]);
}
}  // namespace SuffixArray
int n, m, tot, dp[MAXN][MAXN][2], f[2][MAXN], g[2][MAXN];
char s[2][MAXN], t[MAXN], all[MAXM];
void update(int &x, int y) {
  x += y;
  if (x >= P) x -= P;
}
int solve() {
  tot = 0;
  memset(dp, 0, sizeof(dp));
  for (int i = 1; i <= n; i++) all[++tot] = s[0][i], f[0][i] = tot;
  for (int i = 1; i <= n; i++) all[++tot] = s[1][i], f[1][i] = tot;
  for (int i = 1; i <= m; i++) all[++tot] = t[i], g[0][i] = tot;
  for (int i = m; i >= 1; i--) all[++tot] = t[i], g[1][i] = tot;
  SuffixArray ::init(all, tot);
  int ans = 0;
  for (int i = 1; i <= n + 1; i++) {
    update(dp[i][0][0], 1);
    update(dp[i][0][1], 1);
    for (int j = 2; j <= i - 1 && j * 2 <= m; j++) {
      using namespace SuffixArray;
      if (lcp(g[0][j + 1], f[0][i - j]) >= j && lcp(g[1][j], f[1][i - j]) >= j)
        update(dp[i][j * 2][0], 1);
      if (lcp(g[0][j + 1], f[1][i - j]) >= j && lcp(g[1][j], f[0][i - j]) >= j)
        update(dp[i][j * 2][1], 1);
    }
    for (int j = 0; j <= m - 1; j++) {
      if (t[j + 1] == s[0][i]) {
        update(dp[i + 1][j + 1][0], dp[i][j][0]);
        if (j <= m - 2 && t[j + 2] == s[1][i])
          update(dp[i + 1][j + 2][1], dp[i][j][0]);
      }
      if (t[j + 1] == s[1][i]) {
        update(dp[i + 1][j + 1][1], dp[i][j][1]);
        if (j <= m - 2 && t[j + 2] == s[0][i])
          update(dp[i + 1][j + 2][0], dp[i][j][1]);
      }
    }
    update(ans, dp[i][m][0]);
    update(ans, dp[i][m][1]);
    for (int j = 2; j <= n - i + 1 && j * 2 <= m; j++) {
      using namespace SuffixArray;
      if (lcp(g[0][m - 2 * j + 1], f[0][i]) >= j && lcp(g[1][m], f[1][i]) >= j)
        update(ans, dp[i][m - j * 2][0]);
      if (lcp(g[0][m - 2 * j + 1], f[1][i]) >= j && lcp(g[1][m], f[0][i]) >= j)
        update(ans, dp[i][m - j * 2][1]);
    }
  }
  return ans;
}
int main() {
  scanf("\n%s", s[0] + 1);
  scanf("\n%s", s[1] + 1);
  scanf("\n%s", t + 1);
  n = strlen(s[0] + 1), m = strlen(t + 1);
  int ans = solve();
  reverse(t + 1, t + m + 1);
  update(ans, solve());
  if (m == 1) {
    for (int i = 1; i <= n; i++) {
      update(ans, P - (t[1] == s[0][i]));
      update(ans, P - (t[1] == s[1][i]));
    }
  }
  if (m == 2) {
    for (int i = 1; i <= n; i++) {
      update(ans, P - (t[1] == s[0][i] && t[2] == s[1][i]));
      update(ans, P - (t[1] == s[1][i] && t[2] == s[0][i]));
    }
  } else if (m % 2 == 0) {
    using namespace SuffixArray;
    for (int i = m / 2; i <= n; i++) {
      if (lcp(g[0][m / 2 + 1], f[0][i - m / 2 + 1]) >= m / 2 &&
          lcp(g[1][m / 2], f[1][i - m / 2 + 1]) >= m / 2)
        update(ans, P - 1);
      if (lcp(g[0][m / 2 + 1], f[1][i - m / 2 + 1]) >= m / 2 &&
          lcp(g[1][m / 2], f[0][i - m / 2 + 1]) >= m / 2)
        update(ans, P - 1);
    }
    for (int i = 1; i + m / 2 - 1 <= n; i++) {
      if (lcp(g[0][1], f[0][i]) >= m / 2 && lcp(g[1][m], f[1][i]) >= m / 2)
        update(ans, P - 1);
      if (lcp(g[0][1], f[1][i]) >= m / 2 && lcp(g[1][m], f[0][i]) >= m / 2)
        update(ans, P - 1);
    }
  }
  cout << ans << endl;
  return 0;
}