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: Accepted)

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;
            //先に深い方からやった方が得することがあるかというとそんなことはなくて、そんな暇があったら浅いのをやれてしまうので
            //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;
            }
            //先に浅いのをやることが得になりうるか
            //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 - x.FinalDepth))
            {
                if (depth + item.MinDepth < 0) { Console.WriteLine("No"); return; }
                depth += item.FinalDepth;
            }
            if (depth != 0) { Console.WriteLine("No"); return; }
        }
        //弾かなくて良いものを弾いている
        //throw new Exception();
        Console.WriteLine("Yes");
    }
}

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