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 int Left { get; set; }
        public int Right { get; set; }
    }
    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());
            }

            for(int i = 0; i < N; i++)
            {
                while(str[i].Contains("()"))
                {
                    str[i] = str[i].Replace("()", "");
                }
            }

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

            foreach(var s in str)
            {
                parenthesis += s;
            }

            while(parenthesis.Contains("()"))
            {
                parenthesis = parenthesis.Replace("()", "");
            }

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