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: Wrong Answer)

using System;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            string[] S = new string[N];
            for(int i=0;i<N;i++){
               S[i] = Console.ReadLine();
            }

            int[][] tmp = new int[N][];

            for(int i=0;i<N;i++){
                tmp[i] = CountNum(S[i]);
            }

            Array.Sort(tmp, CompareArray);
            int cur = 0;

            for(int i=0;i<N;i++){
                //選択
                int j=0;
                for(;j<N;j++){
                    int t_t = tmp[j][0];
                    int t_m = tmp[j][1];
                    int t_f = tmp[j][2];

                    if(t_f==1){//既処理はパス
                        
                    }else{
                        if(cur+t_m>=0){
                            cur += t_t;
                            tmp[j][2]=1;
                            break;
                        }
                    }
                }
                if(j==N){
                    Console.WriteLine("No");
                    return;
                }
            }
            if(cur ==0){
                Console.WriteLine("Yes");
            }else{
                Console.WriteLine("No");
            }
        }
        static int CompareArray(int[] x, int[] y)
        {            
            int min = 2;

            for (int n = 0; n < min; n++) {
            if (x[n] > y[n])
                return 1;
            else if (x[n] < y[n])
                return -1;
            }

            if (x.Length > y.Length)
            return 1;
            else if (x.Length < y.Length)
            return -1;
            else /* if (x.Length == y.Length) */
            return 0;
        }
        static int[] CountNum(string s){
            int l = s.Length;
            int min=0;
            int total=0;

            for(int i=0;i<l;i++){
                switch(s[i]){
                    case '(':
                        total += 1;
                        break;
                    case ')':
                        total -= 1;
                        if(min>total){
                            min = total;
                        }
                        break;
                }
            }

            return new int[3]{total,min,0};

        }

    }

}