You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:

* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.



Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.

Constraints

* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.

Examples

Input

3
())


Output

(())


Input

6
)))())


Output

(((()))())


Input

8
))))((((


Output

(((())))(((())))
//
import java.math.*;
import java.util.*;
import java.io.*;
  
public class Main { 
  
    static BufferedReader in;
    static PrintWriter out = new PrintWriter(System.out);
    static String file = "../in";
    static int test = 10; // 0 for local testing, 1 for std input
    static int inf = 1_000_000, mod = 1_000_000_007;

    void swap(int[]ary, int i, int j)
    {
        int t = ary[i];
        ary[i] = ary[j];
        ary[j] = t;
    }
    
    String[] split() throws Exception
    {
        return in.readLine().split(" ");
    }

    int readInt() throws Exception
    {
        return Integer.valueOf(in.readLine());
    }

    int[] toIntArray() throws Exception
    {
        String[] sp = split();
        int n = sp.length;
        int[] ary = new int[n];
        for(int i = 0; i < n; i++) ary[i] = Integer.valueOf(sp[i]);
        return ary;
    }

    long[] toLongArray() throws Exception
    {
        String[] sp = split();
        int n = sp.length;
        long[] ary = new long[n];
        for(int i = 0; i < n; i++) ary[i] = Long.valueOf(sp[i]);
        return ary;
    }

    String reverse(String str)
    {
        return new StringBuilder(str).reverse().toString();
    }

    long choose(int n, int a)
    {
        long nf = 1;
        for(int i = 1; i <= a; i++)
        {
            nf *= i;
            nf %= mod;
            nf *= pow(i, mod - 2);
            nf %= mod;
        }
        return nf;
    }

    long pow(int a, int pow)
    {
        return pow(0L + a, pow);
    }
    
    long pow(long a, int pow)
    {
        long res = 1;
        while(pow > 0)
        {
            if(pow % 2 != 0) {
                res *= a;
                res %= mod;
            }
            a = a * a;
            a %= mod;
            pow /= 2;
        }

        return res;
    }    

    int gcd(int a, int b)
    {
        if(b == 0) return a;
        return gcd(b, a % b);
    }

    public static void main(String[] args) throws Exception
    {
        int _k = Integer.valueOf("1");
        if(test > 0) in = new BufferedReader(new InputStreamReader(System.in));
        else in = new BufferedReader(new FileReader(file));
        if(test < 0) {String[] str = in.readLine().split(" ");}
/***********************************************************************/
/***********************************************************************/
/***********************************************************************/
/***********************************************************************/
        // System.out.println((-100 + 0) / 2);

        new Main().d();
        out.flush();
    }

    void d() throws Exception
    {
        int n = readInt();
        String str = in.readLine();
        int[] marked = new int[n];

        Stack<Integer> stack = new Stack<>();
        for(int i = 0; i < n; i++)
        {
            if(str.charAt(i) == '(') stack.push(i);
            else
            {
                if(!stack.isEmpty()) 
                {
                    marked[stack.pop()]++;
                    marked[i]++;
                }
            }
        }

        StringBuilder sb = new StringBuilder();
        int right = 0;
        for(int i = 0; i < n; i++)
        {
            if(marked[i] > 0) sb.append(str.charAt(i));
            else
            {
                if(str.charAt(i) == ')')
                {
                    sb.insert(0, "(");
                    sb.append(")");
                }
                else
                {
                    sb.append("(");
                    right++;
                }
            }
        }
        while(right-- > 0) sb.append(")");
        System.out.println(sb.toString());
    }

    long count(long[] L, long[] P, long x, int n)
    {
        if(n == 0 && x == 1) return 1;
        if(x <= 1) return 0;
        if(x <= L[n - 1] + 1) return count(L, P, x - 1, n - 1);
        if(x == L[n - 1] + 2) return P[n - 1] + 1;
        if(x <= 2 * L[n - 1] + 2) return P[n - 1] + 1 + count(L, P, x - 2 - L[n - 1], n - 1);
        return P[n];
    }



    int find(int[] f , int p)
    {
        int fp = f[p];
        while(fp != f[fp]) fp = f[f[fp]];
        return f[p] = fp;
    }
}
