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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.io.*;
import java.util.*;
public class Main {

	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] cmd=br.readLine().split(" ");
		int n=Integer.valueOf(cmd[0]);
		int[][] arr=new int[n][2];
		for(int i=0;i<n;i++)
		{
			StringBuilder s=new StringBuilder(br.readLine());
			Stack<Character> st=new Stack<>();
			int cnt=0;
			for(int j=0;j<s.length();j++)
			{
				if(s.charAt(j)=='(')
					st.push('(');
				else
				{
					if(st.empty())
						cnt++;
					else
						st.pop();
				}
			}
			arr[i][1]=st.size();
			arr[i][0]=cnt;
		}
		StringBuilder f=new StringBuilder("");
		for(int i=0;i<n;i++)
		{
			if(arr[i][0]==0)
			{
				for(int j=0;j<arr[i][1];j++)
				{
					f=f.append("(");
				}
			}
		}
		for(int i=0;i<n;i++)
		{
			if(arr[i][1]==0)
			{
				for(int j=0;j<arr[i][0];j++)
				{
					f.append(")");
				}
			}
		}
		for(int i=0;i<n;i++)
		{
			if(arr[i][1]!=0 && arr[i][0]!=0)
			{
				for(int j=0;j<arr[i][0];j++)
				{
					f.append(")");
				}
				for(int j=0;j<arr[i][1];j++)
				{
					f.append("(");
				}
			}
		}
		Stack<Character> st=new Stack<>();
		int b=0;
		for(int i=0;i<f.length();i++)
		{
			if(f.charAt(i)=='(')
				st.push('(');
			else
			{
				if(st.empty())
				{
					b=1;
					break;
				}
				else
					st.pop();
			}
		}
		if(b==1 || st.size()!=0)
			System.out.println("No");
		else
			System.out.println("Yes");
	}

}