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.io.*;
import java.util.*;
import java.math.*;
import java.awt.Point;
 
public class Main {
	//static final long MOD = 998244353L;
	//static final long INF = 1000000000000000007L;
	static final long MOD = 1000000007L;
	static final int INF = 1000000007;
	
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter pw = new PrintWriter(System.out);
		
		int N = sc.ni();
		String s = sc.next();
		int[] pref = new int[N+1];
		int min = 0;
		for (int i = 0; i < N; i++) {
			if (s.charAt(i)=='(')
				pref[i+1] = pref[i]+1;
			else
				pref[i+1] = pref[i]-1;
			min = Math.min(min,pref[i+1]);
		}
		StringBuilder ans = new StringBuilder();
		if (min < 0) {
			for (int i = 0; i < 0-min; i++)
				ans.append('(');
			pref[N] -= min;
		}
		ans.append(s);
		for (int i = 0; i < pref[N]; i++)
			ans.append(')');
		pw.println(ans);
		pw.close();
	}

 
	public static long dist(long[] p1, long[] p2) {
		return (Math.abs(p2[0]-p1[0])+Math.abs(p2[1]-p1[1]));
	}
	
	//Find the GCD of two numbers
	public static long gcd(long a, long b) {
		if (a < b) return gcd(b,a);
		if (b == 0)
			return a;
		else
			return gcd(b,a%b);
	}
	
	//Fast exponentiation (x^y mod m)
	public static long power(long x, long y, long m) { 
		if (y < 0) return 0L;
		long ans = 1;
		x %= m;
		while (y > 0) { 
			if(y % 2 == 1) 
				ans = (ans * x) % m; 
			y /= 2;  
			x = (x * x) % m;
		} 
		return ans; 
	}
	
	public static int[] shuffle(int[] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
	public static long[] shuffle(long[] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
	public static int[][] shuffle(int[][] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
 
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] a, int[] b) {
				  return a[1]-b[1]; //ascending order
	          }
		});
		return array;
	}
    
    public static long[][] sort(long[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<long[]>() {
			  @Override
        	  public int compare(long[] a, long[] b) {
				  if (a[0] < b[0])
					  return -1;
				  else if (a[0] > b[0])
					  return 1;
				  else
					  return 0;
	          }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        }
        
        int ni() { 
            return Integer.parseInt(next()); 
        }
  
        long nl() { 
            return Long.parseLong(next()); 
        } 
  
        double nd() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() {
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str;
        }
    }
}