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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;

public static class P
{
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        Bracket[] brackets = new Bracket[n];
        for (int i = 0; i < n; i++)
        {
            var s = Console.ReadLine();
            int depth = 0;
            int minDepth = 0;
            for (int j = 0; j < s.Length; j++)
            {
                if (s[j] == '(') depth++;
                else depth--;
                minDepth = Min(minDepth, depth);
            }
            brackets[i] = new Bracket() { FinalDepth = depth, MinDepth = minDepth };
        }
        {
            int depth = 0;
            //最初は途中での深さが浅いのから
            foreach (var item in brackets.Where(x => x.FinalDepth >= 0).OrderByDescending(x => x.MinDepth))
            {
                if (depth + item.MinDepth < 0) { Console.WriteLine("No"); return; }
                depth += item.FinalDepth;
            }
            //さっきのの逆、なので途中での深さが深いのから
            foreach (var item in brackets.Where(x => x.FinalDepth < 0).OrderBy(x => x.MinDepth))
            {
                if (depth + item.MinDepth < 0) { Console.WriteLine("No"); return; }
                depth += item.FinalDepth;
            }
            if (depth != 0) { Console.WriteLine("No"); return; }
        }
        throw new Exception();
        Console.WriteLine("Yes");
    }
}

struct Bracket
{
    public int FinalDepth;
    public int MinDepth;
}