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;
using System.Collections.Generic;

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]);
            }

            List<int[]> positiveData = new List<int[]>();//常にプラス
            List<int[]> posinegaData = new List<int[]>();//トータルプラスだが途中マイナス
            List<int[]> negativeData = new List<int[]>();//常にマイナス

            int p=0;
            for(int i=0;i<N;i++){
                if(tmp[i][1]>=0){
                    positiveData.Add(tmp[i]);
                }else if(tmp[i][0]>=0){
                    posinegaData.Add(tmp[i]);
                }else{
                    negativeData.Add(tmp[i]);
                }
                p += tmp[i][0];
            }

            if(p!=0){
                Console.WriteLine("No");
                return;
            }

            IComparer<int[]> ic = new MyComparer();
            posinegaData.Sort(ic);
            negativeData.Sort(ic);

            int cur = 0;   
            for(int i=0;i<positiveData.Count;i++){
                cur += positiveData[i][0];
            }
            for(int i=0;i<posinegaData.Count;i++){
                if(cur+posinegaData[i][1]<0){
                    Console.WriteLine("No");
                    return;
                }else cur += posinegaData[i][0];
            }

            for(int i=0;i<negativeData.Count;i++){
                if(cur+negativeData[i][1]<0){
                    Console.WriteLine("No");
                    return;
                }else{
                    cur = cur+negativeData[i][0];
                }
            }

            Console.WriteLine("Yes");

        }
        
        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};

        }
    }

    class MyComparer : IComparer<int[]>
    {
        public int Compare(int[] x, int[] y)
        {
            return x[1]-y[1];

        }
    }
}