Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3
())

Sample Output 1

(())

Sample Input 2

6
)))())

Sample Output 2

(((()))())

Sample Input 3

8
))))((((

Sample Output 3

(((())))(((())))

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		SC sc = new SC(System.in);
		int N=sc.nextInt();
		String S=sc.next();
		Deque<Integer> tmp=new ArrayDeque<Integer>();
		for(int i=0; i<N; i++) {
			if(S.charAt(i)=='(') {
				tmp.offer(0);
			}
			else if(S.charAt(i)==')') {
				if(tmp.size()==0) {
					tmp.offer(1);
				}
				else {
					if(tmp.peek()==0) {
						tmp.remove();
					}
					else {
						tmp.offer(1);
					}
				}
			}
		}
		int mae=0;
		int ato=0;
		int size=tmp.size();
		//pl(size);
		for(int i=0; i<size; i++) {
			int get=tmp.poll();
			if(get==0) {
				ato++;
			}
			else if(get==1) {
				mae++;
			}
		}
		StringBuilder sb=new StringBuilder();
		for(int i=0; i<mae; i++) {
			sb.append("(");
		}
		sb.append(S);
		for(int i=0; i<ato; i++) {
			sb.append(")");
		}
		pl(sb.toString());

	}

	public static void pl(Object o) {
		System.out.println(o);
	}
	public static void pl() {
		System.out.println();
	}
	public static void p(Object o) {
		System.out.print(o);
	}
	static class SC {
		private BufferedReader reader = null;
		private StringTokenizer tokenizer = null;
		public SC(InputStream in) {
			reader = new BufferedReader(new InputStreamReader(in));
		}
		public String next() {
			if (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new UncheckedIOException(e);
			}
		}
	}
}