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 C# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int M = 1000010;
		string[]S = new string[N];
		int[][] T = new int[N][];
		var listP = new List<int>();
		var listM = new List<int>();
		for(var i=0;i<N;i++){
			S[i] = Console.ReadLine();
			T[i] = new int[3]{0,0,0};
			int min = 0;
			int sum = 0;
			for(var j=0;j<S[i].Length;j++){
				if(S[i].Substring(j,1)=="("){
					sum++;
				} else {
					sum--;
				}
				min = Math.Min(sum,min);
			}
			T[i][0] = i;
			T[i][1] = min;
			T[i][2] = sum;
			if(sum>0){
				listP.Add(i);
			} else {
				listM.Add(i);
			}
		}
		listP.Sort((x,y)=>(T[x][1]*10000000-T[x][2]).CompareTo(T[y][1]*10000000-T[y][2]));
		listM.Sort((x,y)=>(-T[x][1]*10000000-T[x][2]).CompareTo(-T[y][1]*10000000-T[y][2]));
		int sumA = 0;
		string ans = "Yes";
		for(var i=0;i<listP.Count;i++){
			var ia = listP[i];
			if(T[ia][1] < 0 && sumA < -T[ia][1]){
				ans = "No";
			}
			sumA += T[ia][2];
		}
		for(var i=0;i<listM.Count;i++){
			var ia = listM[i];
			if(T[ia][1] < 0 && sumA < -T[ia][1]){
				ans = "No";
			}
			sumA += T[ia][2];
		}
		if(sumA != 0){
          ans = "No";
        }
		Console.WriteLine(ans);
	}
}