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# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp4
{

    class Program
    {


        static void Main()
        {
            int N = Console.Read();
            string[] S = new string[N];
            int answer = 0;
            int start = 0;
            int end = 0;
            int a = 0;
            for(int i = 0; i < S.Length; i++)
            {
                S[i] = Console.ReadLine();
                string nowS = S[i];
               for(int i1 = 0; i1 < S[i].Length; i1++)
                {
                    if (nowS[i1] == '(')
                    {
                        answer = answer + 1;
                    }
                    else
                    {
                        answer = answer - 1;
                    }
                   
                }
                if (nowS[0] == ')')
                {
                    start = start + 1;
                }
                else { }
                if (nowS[nowS.Length-1] == '(')
                {
                    end = end + 1;
                }
                if (nowS[0] == ')' && nowS[nowS.Length - 1] == '(')
                {
                    a = a + 1;
                }

            }
            if (answer == 0&&start!=N&&end!=N&&a!=N&&a!=N-1)
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }

                
            
        }
    }
}