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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

class Main {
	public static void main(String[] args){
		Main.exec4();
	}
	
	static void exec1(){
		// http://abc064.contest.atcoder.jp/tasks/abc064_a
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String s;
		try {
			s = new String(in.readLine());
			s = s.replaceAll(" ", "");
			int i = Integer.parseInt(s);
			String opt;
			if(i%4 == 0) opt = "YES";
			else opt = "NO";
			System.out.println(opt);
		} catch (IOException e) {
			// TODO 自動生成された catch ブロック
			e.printStackTrace();
		}
	}
	
	static void exec2(){
		// http://abc064.contest.atcoder.jp/tasks/abc064_b
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String n_str, a_str;
		try {
			n_str = new String(in.readLine());
			a_str = new String(in.readLine());
			int n = Integer.parseInt(n_str);
			if(n<1 || n>100) throw new Exception();
			String[] a_str_arr = a_str.split(" ", 0);
			if(n != a_str_arr.length) throw new Exception();
			int max=0;
			int min=1000;
			for(int i=0; i<a_str_arr.length; i++){
				int a = Integer.parseInt(a_str_arr[i]);
				if(a<0 || a>1000) throw new Exception();
				if(max<a) max = a;
				if(min>a) min = a;
			}
			System.out.println(max-min);
			
		} catch (IOException e) {
			// TODO 自動生成された catch ブロック
			e.printStackTrace();
		} catch (Exception e) {
			// TODO 自動生成された catch ブロック
			e.printStackTrace();
		}
	}
	
	static void exec3(){
		// http://abc064.contest.atcoder.jp/tasks/abc064_c
		int[] color_rate = {400, 800, 1200, 1600, 2000, 2400, 2800, 3200, 4800};
		Boolean[] is_choosen_arr = new Boolean[8];
		Arrays.fill(is_choosen_arr, false);
		
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String n_str, a_str;
		try {
			n_str = new String(in.readLine());
			a_str = new String(in.readLine());
			int n = Integer.parseInt(n_str);
			if(n<1 || n>100) throw new Exception();
			String[] a_str_arr = a_str.split(" ", 0);
			if(n != a_str_arr.length) throw new Exception();
			
			int free_count = 0;
			for(int i=0; i<a_str_arr.length; i++){
				int a = Integer.parseInt(a_str_arr[i]);
				if(a<1 || a>4800) throw new Exception();
				for(int k=0; k<is_choosen_arr.length; k++){
					if(a < color_rate[k]){
						is_choosen_arr[k] = true;
						break;
					}
				}
				if(a >= color_rate[7]) free_count++;
			}
			int chosen_count = 0;
			for(int i=0; i<is_choosen_arr.length; i++){
				if(is_choosen_arr[i]) chosen_count++;
			}
			
			int min = chosen_count!=0 ? chosen_count: 1;
			int max = chosen_count+free_count;
			
			System.out.println(min + " " + max);
			
		} catch (IOException e) {
			e.printStackTrace();
		} catch (Exception e) {
			e.printStackTrace();
		}
	}
	
	static void exec4(){
		// http://abc064.contest.atcoder.jp/tasks/abc064_d
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String n_str, a_str;
		try {
			n_str = new String(in.readLine());
			a_str = new String(in.readLine());
			int n = Integer.parseInt(n_str);
			if(n<1 || n>100) throw new Exception();
			if(n != a_str.length()) throw new Exception();
			
			while(is_valid(a_str) != 0){
				if(is_valid(a_str) < 0) a_str = "(" + a_str;
				if(is_valid(a_str) > 0) a_str = a_str + ")";
			}
			
			System.out.println(a_str);
		} catch (IOException e) {
			e.printStackTrace();
		} catch (Exception e) {
			e.printStackTrace();
		}
	}
	
	static int is_valid(String n){
		String[] arr = n.split("");
		int i = 0;
		for(String a : arr){
			if(a.equals("(")) i++;
			if(a.equals(")")) i--;
			if(i<0) return -1;
		}
		return i;
	}
}
