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.*;
import java.io.PrintWriter;
public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int r=0;
		int l=0;
		for(int i=0; i<n; i++){
			String s=sc.next();
			int tr=0;
			int tl=0;
			for(int j=0; j<s.length(); j++){
				if(s.charAt(j)==')'){
					if(tr>0){
						tr--;
					}else{
						tl++;
					}
				}else{
					tr++;
				}
			}
			int tmpr=0;
			if(l-tr>0){
				l-=tr;
				tr=0;
			}else{
				tr-=l;
				l=0;
				tmpr=tr;
			}
			if(r-tl>0){
				r-=tl;
				tl=0;
			}else{
				tl-=r;
				r=0;
				l+=tl;
			}
			r+=tmpr;
		}
		if(l==0 && r==0){
			System.out.println("Yes");
		}else{
			System.out.println("No");
		}
	}
}