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 <class T = int>
inline T readInt();
inline double readDouble();
inline int readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int getChar();
inline int peekChar();
inline bool seekEof();
inline void skipBlanks();
template <class T>
inline void writeInt(T x, char end = 0, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(double x, int len = 0);
inline void flush();
static struct buffer_flusher_t {
  ~buffer_flusher_t() { flush(); }
} buffer_flusher;
static const int buf_size = 4096;
static unsigned char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline void skipBlanks() {
  while (!isEof() && buf[buf_pos] <= 32U) buf_pos++;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline int readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-')
    s = -1, c = getChar();
  else if (c == '+')
    c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline double readDouble() {
  int s = 1, c = readChar();
  double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 1e-1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = x;
}
inline void flush() {
  if (write_buf_pos) {
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
    fflush(stdout);
  }
}
template <class T>
inline void writeInt(T x, char end, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
  if (end) writeChar(end);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  int t = (int)x;
  writeInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4")
using namespace std;
mt19937 Random(time(0));
const int INF = 1e9 + 10;
const int MOD = 1e9 + 7;
const int P = 239017;
const long long BINF = 1e18 + 10;
void add(int &a, int b) {
  a += b;
  if (a >= MOD) {
    a -= MOD;
  }
}
int get(string s1, string s2) {
  int mn = min((int)s1.size(), (int)s2.size());
  for (int len = mn; len >= 0; len--) {
    bool t = true;
    for (int i = 0; i < len; i++) {
      if (s1[i] != s2[(int)s2.size() - len + i]) {
        t = false;
        break;
      }
    }
    if (t) {
      return len;
    }
  }
}
const int N = 210;
int dp[N][N][N][2], go[N][2];
void source() {
  int n;
  string s;
  cin >> n >> s;
  n *= 2;
  int sz = (int)s.size();
  string cur;
  for (int i = 0; i <= sz; i++) {
    cur += "(";
    go[i][0] = get(s, cur);
    cur[(int)cur.size() - 1] = ')';
    go[i][1] = get(s, cur);
    if (i < sz) {
      cur[(int)cur.size() - 1] = s[i];
    }
  }
  dp[0][0][0][0] = 1;
  for (int i = 0; i < n; i++) {
    for (int balance = 0; balance <= i; balance++) {
      for (int same = 0; same <= sz; same++) {
        int to = go[same][0];
        if (to == sz) {
          add(dp[i + 1][balance + 1][sz][1], dp[i][balance][same][0]);
          add(dp[i + 1][balance + 1][sz][1], dp[i][balance][same][1]);
        } else {
          add(dp[i + 1][balance + 1][to][0], dp[i][balance][same][0]);
          add(dp[i + 1][balance + 1][to][1], dp[i][balance][same][1]);
        }
        if (balance > 0) {
          to = go[same][1];
          if (to == sz) {
            add(dp[i + 1][balance - 1][sz][1], dp[i][balance][same][0]);
            add(dp[i + 1][balance - 1][sz][1], dp[i][balance][same][1]);
          } else {
            add(dp[i + 1][balance - 1][to][0], dp[i][balance][same][0]);
            add(dp[i + 1][balance - 1][to][1], dp[i][balance][same][1]);
          }
        }
      }
    }
  }
  int ans = 0;
  for (int same = 0; same <= sz; same++) {
    add(ans, dp[n][0][same][1]);
  }
  cout << ans;
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  source();
  return 0;
}
