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[][] a = new int[n][2];
        PriorityQueue<int[]> q = new PriorityQueue<>((x,y) -> y[0]-x[0]);
        for (int i = 0; i < n; i++) {
            char[] s = sc.next().toCharArray();
            int sum = 0;
            int min = 0;
            for (int j = 0; j < s.length; j++) {
                if(s[j] == '(') sum++;
                else sum--;
                min = Math.min(min, sum);
            }
            a[i][0] = sum;
            a[i][1] = min;
            q.add(a[i]);
        }
        int sum = 0;
        boolean ok = true;
        List<int[]> list = new ArrayList<>();
        while(!q.isEmpty()){
            int[] x = q.poll();
            if(sum + x[1] < 0){
                list.add(x);
            }else{
                sum += x[0];
                if(!list.isEmpty()){
                    q.addAll(list);
                    list.clear();
                }
            }
        }
        if(!list.isEmpty()) ok = false;
        System.out.println(ok && sum == 0 ? "Yes" : "No");
        sc.close();

    }

}