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>
template <typename T>
void MACRO_VAR_Scan(T& t) {
  std::cin >> t;
}
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First& first, Rest&... rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
template <typename T>
void MACRO_VEC_ROW_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T>
void MACRO_VEC_ROW_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
template <typename T>
inline T CHMAX(T& a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T>
inline T CHMIN(T& a, const T b) {
  return a = (a > b) ? b : a;
}
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n";
}
template <class T>
std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;
constexpr int INFINT_LIM = (1LL << 31) - 1;
constexpr ll INFLL = 1LL << 60;
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);
constexpr double EPS = 1e-9;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N>
void FILL(T (&a)[N], const T& val) {
  for (auto& x : a) x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T& val) {
  for (auto& b : a) FILL(b, val);
}
template <class T>
void FILL(std::vector<T>& a, const T& val) {
  for (auto& x : a) x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>>& a, const T& val) {
  for (auto& b : a) FILL(b, val);
}
int dp[202][202][202];
int dp2[202];
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  int n;
  MACRO_VAR_Scan(n);
  ;
  std::string s;
  MACRO_VAR_Scan(s);
  ;
  int sz = s.size();
  dp2[0] = 0;
  {
    for (int i = (1); i < (sz); ++i) {
      auto t(s);
      t[i] = (s[i] == ')') ? '(' : ')';
      for (int j = (i + 1) - 1; j >= (1); --j) {
        if (s.substr(0, j) == t.substr(i - j + 1, j)) {
          dp2[i] = j;
          break;
        }
      }
    }
  }
  dp[0][0][0] = 1;
  for (int i = 0; i < int(2 * n); ++i)
    for (int j = 0; j < int(sz + 1); ++j)
      for (int k = 0; k < int(2 * n + 1); ++k) {
        if (dp[i][j][k] == 0) continue;
        if (j == sz) {
          (dp[i + 1][sz][k + 1] += dp[i][j][k]) %= MOD;
          if (k - 1 >= 0) (dp[i + 1][sz][k - 1] += dp[i][j][k]) %= MOD;
        } else {
          {
            if (s[j] == '(') {
              (dp[i + 1][j + 1][k + 1] += dp[i][j][k]) %= MOD;
            } else {
              (dp[i + 1][dp2[j]][k + 1] += dp[i][j][k]) %= MOD;
            }
          }
          if (k - 1 >= 0) {
            if (s[j] == ')') {
              (dp[i + 1][j + 1][k - 1] += dp[i][j][k]) %= MOD;
            } else {
              (dp[i + 1][dp2[j]][k - 1] += dp[i][j][k]) %= MOD;
            }
          }
        }
      }
  std::cout << (dp[2 * n][sz][0]);
  std::cout << "\n";
  ;
  return 0;
}
