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];
		var list = new List<int>[2*M+1];
		var listB = new List<int>[2*M+1];
		for(var i=0;i<=2*N;i++){
			list[i] = new List<int>();
			listB[i] = new List<int>();
		}
		int[][]T = new int[N][];
		int[]TCP = new int[2*M+1];
		int[]TCM = new int[2*M+1];
		int[]TSP = new int[2*M+1];
		int[]TSM = new int[2*M+1];
		int Pct = 0;
		var listT = new List<int>();
		int sumA = 0;
		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){
				TSP[M+min] += sum;
				TCP[M+min] += 1;
				Pct++;
			} else {
				TSM[M+min] += sum;
				TCM[M+min] += 1;
			}
		}
		int m1 = 0;
		int m2 = N;
		int ct = 0;
		string ans = "Yes";
 		//for(var i=N;i>=-N;i--){
		//	Console.Error.WriteLine(N+i+" "+TCP[N+i]+" "+TSP[N+i]+" "+TCM[N+i]+" "+TSM[N+i]);
        //}
		while(ct < Pct){
			int nct = 0;
			for(var i=m1;i<=m2;i++){
				ct += TCP[M+i];
				nct += TCP[M+i];
				sumA += TSP[M+i];
			}
			if(nct==0 && ct < nct){
				ans = "No";
				break;
			}
			m2 = m1-1;
			m1 = -sumA;
		}
		//Console.Error.WriteLine(sumA);
		for(var i=N;i>=-N;i--){
			for(var j=0;j<TCM[M+i];j++){
				if(sumA < -i){
					ans = "No";
				}
			}
			sumA -= TSM[M+i];
			if(sumA < 0){
				ans = "No";
			}
		}
		if(sumA != 0){
          ans = "No";
        }
		Console.WriteLine(ans);
	}
}