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# (Mono-mcs 6.8.0.105) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {

            int N = GetInt();
            long K = GetLong();
            int[] A = GetInts(N);

            int Start = 0;
            int Next = new int();

            bool[] Set = new bool[N];
            Set[0] = true;
            int count = 0;

            for (int i = 0; i < N; i++)
            {
                Next = A[Start];
                Start = Next - 1;
                if (Set[Start] == true)
                {
                    count++;
                    break;
                }
                Set[Start] = true;
                count++;
            }

            int pos = Start;
            int toPos = 0;

            Start = 0;

            for (int i = 0; i < N; i++)
            {
                if (Start == pos)
                {
                    toPos = i;
                    break;
                }
                Next = A[Start];
                Start = Next - 1;
            }

            long loop = count - toPos;

            K -= toPos;
            K %= loop;
            K += toPos;

            Start = 0;
            for (int i = 0; i < K; i++)
            {
                Next = A[Start];
                Start = Next - 1;
            }

            Console.WriteLine(Next);

            return;
        }
    }
}


public static class MyIO
{
    private static string[] args = null;
    private static int num = -1;
    private static int used = -1;

    private static string getArg()
    {
        if (used == num)
        {
            args = Console.ReadLine().Split(' ');
            num = args.Length;
            used = 0;
        }
        return args[used++];
    }

    public static int GetInt() => int.Parse(getArg());
    public static long GetLong() => long.Parse(getArg());
    public static double GetDouble() => double.Parse(getArg());
    public static string GetString() => getArg();
    public static char GetChar() => getArg()[0];
    public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
    public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
    public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
    public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}