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 ConsoleApp28
{
    class Parenthesis
    {
        public static int CountChar(string str)
        {
            int min = int.MaxValue;
            int open = 0;
            int close = 0;
            for (int i = 0; i < str.Length; i++)
            {
                if (str[i] == '(')
                    open++;
                else if (str[i] == ')')
                    close++;
                min = open - close < min ? open - close : min;
            }

            return min;
        }
    }
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            var str = new List<string>();
            for(int i = 0; i < N; i++)
            {
                str.Add(Console.ReadLine());
            }
            //)((((
            
            var comp = new StringComparer();

            str.Sort(comp);
            string parenthesis = "";

            foreach(var s in str)
            {
                parenthesis += s;
            }
            int min;
            int open;
            
            min = Parenthesis.CountChar(parenthesis);

            Console.WriteLine(min == 0 ? "Yes" : "No" );
        }

        public static (int min, int open, int close) CountChar(string str)
        {
            int min = int.MaxValue;
            int open = 0;
            int close = 0;
            for(int i = 0; i < str.Length; i++)
            {
                if (str[i] == '(')
                    open++;
                else if (str[i] == ')')
                    close++;
                min = open - close < min ? open - close : min;
            }

            return (min, open, close);
        }
        
    }
    public class StringComparer : IComparer<string>

    {
        public int Compare(string str1, string str2)
        {
            var min_open_surplus = new int[2];
            var open = new int[2];
            var close = new int[2];
            
            (min_open_surplus[0], open[0], close[0]) = Program.CountChar(str1);
            (min_open_surplus[1], open[1], close[1]) = Program.CountChar(str2);

            if (min_open_surplus[0] >= 0 && min_open_surplus[1] < 0)
            {
                return - 1;
            }
            else if (min_open_surplus[0] < 0 && min_open_surplus[1] >= 0)
            {
                return 1;
            }
            else if (min_open_surplus[0] >= 0 && min_open_surplus[1] >= 0)
            {
                return close[0] - close[1];
            }
            else
            {
                return open[1] - open[0];
            }
        }
    }
}