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.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {

        new Main().go();
    }

    PrintWriter out;
    Reader in;
    BufferedReader br;

    Main() throws IOException {

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            //in = new Reader("input.txt");
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }
    }

    void go() throws Exception {

        //int t = in.nextInt();
        int t = 1;
        while (t > 0) {
            solve();
            t--;
        }

        out.flush();
        out.close();
    }


    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.000000001;

    int n;
    int m;

    ArrayList<Pair>[] g;
    String s;
    int[] maxPref = new int[200];
    void solve() throws IOException {
        n = in.nextInt();
        s = in.nextLine();

        StringBuilder sb = new StringBuilder();
        sb.append(s.charAt(0));
        for (int i = 1; i < s.length(); i++) {
            char br = '(';
            if (s.charAt(i) == '(') br = ')';
            String t = sb.toString() + br;
            for (int j = 1; j < t.length(); j++) {
                boolean ok = true;
                int pos = 0;
                for (int k = j; k < t.length(); k++) {
                    ok &= s.charAt(pos) == t.charAt(k);
                    pos++;
                }
                if (ok) {
                    maxPref[i] = t.length() - j;
                    break;
                }
            }
            sb.append(s.charAt(i));
        }

        out.println(f(0, 0,0));
    }

    int cnt(int start, String sub, int n) {
        int[][] dp = new int[n][n];
        boolean[][] used = new boolean[n][n];
        for (int i = 0; i < n; i++) {
            boolean any = i < start || i >= start + sub.length();
            for (int j = 0; j <= n / 2; j++) {
                if (i == 0) {
                    if (any || sub.charAt(0) == '(') {
                        dp[0][1] = 1;
                        used[0][1] = true;
                    }
                    continue;
                }

                if (any || sub.charAt(i - start) == '(') {
                    if (used[i - 1][j]) {
                        dp[i][j + 1] = (dp[i][j + 1] + dp[i - 1][j]) % mod;
                        used[i][j + 1] = true;
                    }
                }

                if (any || sub.charAt(i - start) == ')') {
                    if (j > 0 && used[i - 1][j]) {
                        dp[i][j - 1] = (dp[i][j - 1] + dp[i - 1][j]) % mod;
                        used[i][j - 1] = true;
                    }
                }
            }
        }
        return dp[n - 1][0];
    }

    int[][][] dp = new int[200][101][201];
    boolean[][][] used = new boolean[200][101][201];
    int f(int pos, int balance, int pref) {

        if (balance < 0 || balance > n)
            return 0;

        if (pos == n * 2) {
            return balance == 0 && pref == s.length() ? 1 : 0;
        }

        if (used[pos][balance][pref])
            return dp[pos][balance][pref];

        int res = 0;
        if (pref == s.length()) {
            res = f(pos + 1, balance + 1, pref)
                    + f(pos + 1, balance - 1, pref);
        } else {
            if (s.charAt(pref) == '(') {
                res += f(pos + 1, balance + 1, pref + 1);
                res += f(pos + 1, balance - 1, maxPref[pref]);
            }
            else {
                res += f(pos + 1, balance - 1, pref + 1);
                res += f(pos + 1, balance + 1, maxPref[pref]);
            }
        }

        dp[pos][balance][pref] = res % mod;
        used[pos][balance][pref] = true;
        return dp[pos][balance][pref];
    }

    class Pair implements Comparable<Pair>{

        int a;
        int b;

        Pair(int a, int b) {

            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {
            if (a != p.a)
                return Integer.compare(a, p.a);
            else
                return Integer.compare(b, p.b);
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }


    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

    }

    static class InputReader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public InputReader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

}