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>
const long long maxn = 2e2 + 1e2;
const long long mod = 1e9 + 7;
static long long dp[maxn][maxn];
static long long dp2[maxn][maxn][maxn];
long long jump[maxn][2];
bool valid[maxn];
int main() {
  std::ios::sync_with_stdio(false);
  long long n;
  std::cin >> n;
  n *= 2;
  std::string s;
  std::cin >> s;
  long long lowest_prefix_sum = 0;
  long long final_sum = 0;
  for (char i : s) {
    if (i == '(') {
      final_sum++;
    } else {
      final_sum--;
    }
    lowest_prefix_sum = std::min(lowest_prefix_sum, final_sum);
  }
  memset(jump, -1, sizeof(jump));
  for (int i = 0; i < s.size(); i++) {
    std::string cop;
    if (s[i] == '(') {
      jump[i][0] = i + 1;
      cop = s.substr(0, i) + ')';
      while (!cop.empty() and s.substr(0, cop.size()) != cop) {
        cop.erase(cop.begin());
      }
      jump[i][1] = cop.size();
    } else {
      cop = s.substr(0, i) + '(';
      while (!cop.empty() and s.substr(0, cop.size()) != cop) {
        cop.erase(cop.begin());
      }
      jump[i][0] = cop.size();
      jump[i][1] = i + 1;
    }
  }
  valid[0] = true;
  for (int i = 1; i < s.size(); i++) {
    std::string cop = s.substr(0, i) + s;
    if (cop.substr(0, s.size()) == s) {
      valid[i] = false;
    } else {
      valid[i] = true;
    }
  }
  dp[0][0] = 1;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 0; j <= n; j++) {
      dp[i][j] = 0;
      if (j != n) dp[i][j] += dp[i - 1][j + 1];
      if (j != 0) dp[i][j] += dp[i - 1][j - 1];
      dp[i][j] %= mod;
    }
  }
  dp2[0][0][0] = 1;
  for (long long i = 0; i <= n; i++) {
    for (long long j = 0; j <= n; j++) {
      for (long long k = 0; k < s.size(); k++) {
        if (j != n) {
          dp2[i + 1][j + 1][jump[k][0]] += dp2[i][j][k];
          dp2[i + 1][j + 1][jump[k][0]] %= mod;
        }
        if (j != 0) {
          dp2[i + 1][j - 1][jump[k][1]] += dp2[i][j][k];
          dp2[i + 1][j - 1][jump[k][1]] %= mod;
        }
      }
    }
  }
  long long res = 0;
  for (long long i = 0; i + s.size() <= n; i++) {
    for (long long j = -lowest_prefix_sum; j <= i; j++) {
      for (int k = 0; k < s.size(); k++) {
        if (valid[k]) {
          res += dp2[i][j][k] * dp[n - ((int)s.size()) - i][j + final_sum];
          res %= mod;
        }
      }
    }
  }
  std::cout << res << '\n';
}
