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>
template <typename T>
inline T abs(T a) {
  return a < 0 ? -a : a;
}
template <typename T>
inline T min(T a, T b) {
  return a < b ? a : b;
}
template <typename T>
inline T max(T a, T b) {
  return a > b ? a : b;
}
template <typename T>
inline void swap(T& a, T& b) {
  T t = a;
  a = b, b = t;
}
template <typename T>
inline bool umin(T& mn, T u) {
  return u < mn ? mn = u, true : false;
}
template <typename T>
inline bool umax(T& mx, T u) {
  return u > mx ? mx = u, true : false;
}
template <typename T>
inline void read(T& r) {
  char c;
  r = 0;
  bool flag = false;
  do c = getchar();
  while (c != '-' && (c < '0' || c > '9'));
  if (c == '-') flag = true, c = getchar();
  do r = r * 10 + c - '0', c = getchar();
  while (c >= '0' && c <= '9');
  if (flag) r *= -1;
}
template <typename T>
inline void read(T& r, T& s) {
  read(r), read(s);
}
template <typename T>
inline void read(T& r, T& s, T& t) {
  read(r), read(s), read(t);
}
template <typename T>
inline void read(T& r, T& s, T& t, T& u) {
  read(r), read(s), read(t), read(u);
}
template <typename T>
inline void write(T w, const char* c = "") {
  if (w == 0)
    putchar('0');
  else {
    if (w < 0) putchar('-'), w *= -1;
    static int s[21], top;
    top = 0;
    while (w) s[top++] = w % 10, w /= 10;
    while (top--) putchar(s[top] + '0');
  }
  for (int i = 0; c[i]; i++) putchar(c[i]);
}
const unsigned long long prime = 233;
unsigned long long p[2002], ha[2002], hb[2002], hs[2002], ht[2002];
char a[2002], b[2002], s[2002], t[2002];
int dp[2][4][2002], n, l, xl;
void gethashed(char* s, unsigned long long* h, int n) {
  for (int i = n; i >= 0; i--) h[i] = h[i + 1] + s[i] * p[n - i];
}
inline bool scmp(unsigned long long* a, int q, int r, unsigned long long* b,
                 int s, int t) {
  if (q < 0 || s < 0 || r > n || t > l) return false;
  unsigned long long idxa = (a[q] - a[r]) * p[q];
  unsigned long long idxb = (b[s] - b[t]) * p[s];
  return idxa == idxb;
}
int ans = 0;
const int mod = 1e9 + 7;
inline void cut(int& first) {
  if (first >= mod) first -= mod;
}
inline void fill(int& first) {
  if (first < 0) first += mod;
}
void work() {
  int i, j;
  bool cur = 1, nxt = 0;
  dp[0][0][0] = dp[0][1][0] = dp[0][2][0] = dp[0][3][0] = 1;
  for (i = 0; i <= n; i++) {
    cur ^= 1, nxt ^= 1;
    cut(ans += dp[cur][0][l]), cut(ans += dp[cur][1][l]),
        cut(ans += dp[cur][2][l]), cut(ans += dp[cur][3][l]);
    for (j = 2; j <= xl; j++)
      if (!scmp(hb, i, i + j, ht, 0, j))
        break;
      else if (scmp(ha, i, i + j, hs, l - j - j, l - j))
        cut(ans += dp[cur][0][l - j - j]);
    for (j = 2; j <= xl; j++)
      if (!scmp(ha, i, i + j, ht, 0, j))
        break;
      else if (scmp(hb, i, i + j, hs, l - j - j, l - j))
        cut(ans += dp[cur][1][l - j - j]);
    for (j = 2; j <= xl; j++)
      if (!scmp(hb, i, i + j, hs, 0, j))
        break;
      else if (scmp(ha, i, i + j, ht, l - j - j, l - j))
        cut(ans += dp[cur][2][l - j - j]);
    for (j = 2; j <= xl; j++)
      if (!scmp(ha, i, i + j, hs, 0, j))
        break;
      else if (scmp(hb, i, i + j, ht, l - j - j, l - j))
        cut(ans += dp[cur][3][l - j - j]);
    if (l % 2 == 0) {
      if (scmp(ha, i - xl, i, hs, xl, l) && scmp(hb, i - xl, i, ht, xl, l))
        fill(--ans);
      if (scmp(ha, i - xl, i, ht, xl, l) && scmp(hb, i - xl, i, hs, xl, l))
        fill(--ans);
      if (xl != 1 && scmp(ha, i, i + xl, hs, 0, xl) &&
          scmp(hb, i, i + xl, ht, 0, xl))
        fill(--ans);
      if (xl != 1 && scmp(ha, i, i + xl, ht, 0, xl) &&
          scmp(hb, i, i + xl, hs, 0, xl))
        fill(--ans);
    }
    if (i == n) break;
    for (j = 0; j <= l; j++)
      dp[nxt][0][j] = dp[nxt][1][j] = dp[nxt][2][j] = dp[nxt][3][j] = 0;
    i++;
    for (j = 0; j <= xl; j++)
      if (j != 1)
        if (!scmp(hb, i - j, i, ht, l - j, l))
          break;
        else if (scmp(ha, i - j, i, hs, j, j << 1))
          cut(++dp[nxt][0][j << 1]);
    for (j = 0; j <= xl; j++)
      if (j != 1)
        if (!scmp(ha, i - j, i, ht, l - j, l))
          break;
        else if (scmp(hb, i - j, i, hs, j, j << 1))
          cut(++dp[nxt][1][j << 1]);
    for (j = 0; j <= xl; j++)
      if (j != 1)
        if (!scmp(hb, i - j, i, hs, l - j, l))
          break;
        else if (scmp(ha, i - j, i, ht, j, j << 1))
          cut(++dp[nxt][2][j << 1]);
    for (j = 0; j <= xl; j++)
      if (j != 1)
        if (!scmp(ha, i - j, i, hs, l - j, l))
          break;
        else if (scmp(hb, i - j, i, ht, j, j << 1))
          cut(++dp[nxt][3][j << 1]);
    i--;
    for (j = 0; j < l; j++)
      if (dp[cur][0][j])
        if (a[i] == s[j]) {
          cut(dp[nxt][0][j + 1] += dp[cur][0][j]);
          if (b[i] == s[j + 1]) cut(dp[nxt][1][j + 2] += dp[cur][0][j]);
        }
    for (j = 0; j < l; j++)
      if (dp[cur][1][j])
        if (b[i] == s[j]) {
          cut(dp[nxt][1][j + 1] += dp[cur][1][j]);
          if (a[i] == s[j + 1]) cut(dp[nxt][0][j + 2] += dp[cur][1][j]);
        }
    for (j = 0; j < l; j++)
      if (dp[cur][2][j])
        if (a[i] == t[j]) {
          cut(dp[nxt][2][j + 1] += dp[cur][2][j]);
          if (b[i] == t[j + 1]) cut(dp[nxt][3][j + 2] += dp[cur][2][j]);
        }
    for (j = 0; j < l; j++)
      if (dp[cur][3][j])
        if (b[i] == t[j]) {
          cut(dp[nxt][3][j + 1] += dp[cur][3][j]);
          if (a[i] == t[j + 1]) cut(dp[nxt][2][j + 2] += dp[cur][3][j]);
        }
  }
}
int main() {
  scanf("%s%s%s", a, b, s);
  n = strlen(a), l = strlen(s), xl = l >> 1;
  int maxl = max(n, l);
  p[maxl] = 1;
  for (int i = maxl - 1; i >= 0; i--) p[i] = p[i + 1] * prime;
  strcpy(t, s);
  std::reverse(t, t + l);
  gethashed(a, ha, maxl);
  gethashed(b, hb, maxl);
  gethashed(s, hs, maxl);
  gethashed(t, ht, maxl);
  work();
  if (l == 1) ans >>= 1;
  write(ans);
  return 0;
}