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.util.*;
import java.io.*;
import java.math.*;


import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;


public class Main{ 


    static long mod=1000000007;
     static int dx[]={1,-1,0,0};
       static int dy[]={0,0,1,-1};
    // static int dx[]={1,-1,0,0,1,1,-1,-1};
    // static int dy[]={0,0,1,-1,1,-1,1,-1};
    // PriorityQueue<Integer> que = new PriorityQueue<Integer>(); 
    //HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();

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

    
    Reader sc = new Reader(System.in);
    PrintWriter out=new PrintWriter(System.out);

    //  int n=sc.nextInt();  
    int n=sc.nextInt();
    // int k=sc.nextInt();
    String s=sc.nextString(), l="";
    char c[] = s.toCharArray();
    int balance=0;

    for( int i=0; i<n; i++ ){
        if(c[i]==')' ){
            balance--;
        }
        else balance++;
        if(balance < 0){
            balance = 0;
            l+="(";
        }
    }

    for( int i=0; i<balance; i++ ){
        s=s+")";
    }

    out.println(l+s);
    out.flush();
}

static void db(Object... os){

    System.err.println(Arrays.deepToString(os));

}

static boolean validpos(int x,int y,int r, int c){
    
    return x<r && 0<=x && y<c && 0<=y;
    
}
 
static boolean bit(long x,int k){
    // weather k-th bit (from right) be one or zero
    return  ( 0 < ( (x>>k) & 1 )  )  ? true:false;
}

}


class XY {
    int x,y,d;
    XY(int x, int y, int d) {
        this.x=x;
        this.y=y;
        this.d=d;
    } 
}

class P implements Comparable<P>{
    int x,y;
    P(int x, int y) {
        this.x=x;
        this.y=y;
    } 
      
    public int compareTo(P p){
        return x - p.x;
    } 
}



class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}

