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 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
	static class Bracket {
		int diff;
		int bottom;
		public Bracket(int diff, int bottom) {
			this.diff = diff;
			this.bottom = bottom;
		}
		
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		ArrayList<Bracket> list1 = new ArrayList<>();
		ArrayList<Bracket> list2 = new ArrayList<>();
		for(int i=0; i<N; i++) {
			char[] c = sc.next().toCharArray();
			int cur = 0;
			int bottom = 0;
			for(int j=0; j<c.length; j++) {
				if(c[j]=='(') {
					cur++;
				} else {
					cur--;
					bottom = Math.min(bottom, cur);
				}
			}
			if(cur >= 0)
				list1.add(new Bracket(cur, bottom));
			else
				list2.add(new Bracket(cur, bottom));
				
		}
		
		Collections.sort(list1, new Comparator<Bracket>() {
			public int compare(Bracket b1, Bracket b2) {
				return - Integer.compare(b1.bottom, b2.bottom);
			}
		});
		
		int pos = 0;

		for(Bracket b : list1) {
			if(pos + b.bottom < 0) {
				System.out.println("No");
				sc.close();
				return;
			}
			pos += b.diff;
		}

		Collections.sort(list2, new Comparator<Bracket>() {
			public int compare(Bracket b1, Bracket b2) {
				return Integer.compare(b1.bottom, b2.bottom);
			}
		});
		for(Bracket b : list2) {
			if(pos + b.bottom < 0) {
				System.out.println("No");
				sc.close();
				return;
			}
			pos += b.diff;
		}
		
		if(pos != 0) {
			System.out.println("No");
			sc.close();
			return;
		}

		System.out.println("Yes");
		sc.close();
	}

}