You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.

Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).

Input

The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).

The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).

Output

Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).

Examples

Input

5
()))()


Output

5


Input

3
(()


Output

4


Input

2
(((


Output

0

Note

All regular bracket sequences satisfying the conditions above for the first example: 

  * "(((()))())"; 
  * "((()()))()"; 
  * "((()))()()"; 
  * "(()(()))()"; 
  * "()((()))()". 



All regular bracket sequences satisfying the conditions above for the second example: 

  * "((()))"; 
  * "(()())"; 
  * "(())()"; 
  * "()(())". 



And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example.
#include <bits/stdc++.h>
using namespace std;
char buf[25];
const int mod = 1000000007;
const int maxn = 210;
int a[maxn], w[maxn][2], g[maxn][maxn], f[maxn][maxn][maxn];
int n, m, ans;
int read() {
  int x = 0, f = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = 1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return f ? -x : x;
}
void write(int x) {
  if (!x) {
    putchar('0');
    return;
  }
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  int cnt = 0;
  while (x) {
    buf[++cnt] = '0' + x % 10;
    x /= 10;
  }
  for (int i = cnt; i >= 1; --i) putchar(buf[i]);
}
bool pd(int l1, int r1, int l2, int r2) {
  for (int i = l1; i <= r1; ++i)
    if (a[i] != a[i + l2 - l1]) return false;
  return true;
}
void Getline() {
  char ch = getchar();
  while (ch != '(' && ch != ')') ch = getchar();
  while (ch == '(' || ch == ')') {
    a[++m] = (ch == '(' ? 0 : 1);
    ch = getchar();
  }
  for (int i = 0; i <= m - 1; ++i)
    for (int j = 0; j <= 1; ++j) {
      if (a[i + 1] == j)
        w[i][j] = i + 1;
      else {
        for (int k = i; k >= 1; --k)
          if (a[k] == j && pd(1, k - 1, i - k + 2, i)) {
            w[i][j] = k;
            break;
          }
      }
    }
}
int main() {
  n = read();
  Getline();
  f[0][0][0] = 1;
  g[0][0] = 1;
  for (int i = 0; i <= n * 2; ++i)
    for (int j = 0; j <= i; ++j)
      for (int tw = 0; tw <= 1; ++tw)
        if (j + (tw == 0 ? 1 : -1) >= 0)
          (g[i + 1][j + (tw == 0 ? 1 : -1)] += g[i][j]) %= mod;
  for (int i = 0; i <= n * 2; ++i)
    for (int j = 0; j <= i; ++j)
      for (int k = 0; k <= min(i, m); ++k)
        if (f[i][j][k]) {
          if (k == m) {
            ans = (ans + 1ll * f[i][j][k] * g[n * 2 - i][j] % mod) % mod;
            continue;
          }
          for (int tw = 0; tw <= 1; ++tw)
            if (j + (tw == 0 ? 1 : -1) >= 0)
              (f[i + 1][j + (tw == 0 ? 1 : -1)][w[k][tw]] += f[i][j][k]) %= mod;
        }
  write(ans);
  putchar('\n');
  return 0;
}
