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.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScan in = new MyScan(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        public void solve(int testNumber, MyScan in, PrintWriter out) {
            int n = in.nextInt();
            String pos = in.next();
            int[][] auto = toAuto(pos);

            long[][][] state = new long[2 * n + 1][2 * n + 1][pos.length() + 1];
            long[][] ansFull = new long[2 * n + 1][2 * n + 1];


            for (int s = 0; s <= n; s++) {
                long[][] starts = new long[2 * n + 1][2 * n + 1];
                starts[0][s] = 1;
                for (int len = 0; len < 2 * n; len++) {
                    for (int gand = 0; gand <= n; gand++) {
                        if (gand > 0) {
                            starts[len + 1][gand - 1] = (starts[len + 1][gand - 1] + starts[len][gand]) % Util._m;
                        }
                        starts[len + 1][gand + 1] = (starts[len + 1][gand + 1] + starts[len][gand]) % Util._m;
                    }
                }
                for (int r = 0; r <= 2 * n; r++) {
                    ansFull[r][s] = starts[r][0];
                }

            }

            state[0][0][0] = 1;
            long res = 0;
            for (int px = 0; px < 2 * n; px++) {
                for (int l = 0; l < 2 * n; l++) {
                    for (int s = 0; s < pos.length(); s++) {
                        int next0 = auto[s][0];
                        int next1 = auto[s][1];
                        // (
                        state[px + 1][l + 1][next0] = (state[px + 1][l + 1][next0] + state[px][l][s]) % Util._m;
                        // )
                        if (l > 0)
                            state[px + 1][l - 1][next1] = (state[px + 1][l - 1][next1] + state[px][l][s]) % Util._m;
                    }
                }
                for (int l = 0; l < 2 * n; l++) {
                    int l2 = 2 * n - px - 1;
                    int n2 = l;
                    if (state[px + 1][l][pos.length()] == 0 || n2 > l2) continue;
                    res += state[px + 1][l][pos.length()] * ansFull[l2][n2] % Util._m;
                }
            }
            out.println(res % Util._m);
        }

        private int[][] toAuto(String pos) {
            int[][] r = new int[pos.length()][2];

            String chars = "()";
            for (int t = 0; t < pos.length(); t++) {
                for (int i = 0; i < chars.length(); i++) {
                    char ch = chars.charAt(i);
                    if (pos.charAt(t) == ch) {
                        r[t][i] = t + 1;
                    } else {
                        String tar = pos.substring(0, t) + ch;
                        for (int l = t; l > 0; l--) {
                            if (tar.endsWith(pos.substring(0, l))) {
                                r[t][i] = l;
                                break;
                            }
                        }
                    }
                }
            }

            return r;
        }

    }

    static class MyScan {
        private final InputStream in;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0;
        public int ptrbuf = 0;

        public MyScan(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = in.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

    }

    static class Util {
        public static final long M07 = 1000_000_007;
        public static final long _m = M07;

    }
}

