Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[][] x = new int[N][2];
		for(int i = 0; i < N; i++) {
			String S = sc.next();
			int l = 0, r = 0;
			for(int j = 0; j < S.length(); j++) {
				if(S.charAt(j) == '(')
					l++;
				else {
					if(l > 0)
						l--;
					else
						r++;
				}
			}
			x[i][0] = l;
			x[i][1] = r;
		}
		Arrays.sort(x, (a, b) -> a[1] - b[1]);
		int l = 0, r = 0;
		boolean ok = true;
		for(int i = 0; i < N; i++) {
			l -= x[i][1];
			if(l < 0) {
				ok = false;
				break;
			}
			l += x[i][0];
		}
		System.out.println(ok && l == 0 ? "Yes" : "No");
	}

}