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 {
//    static PrintWriter out = new PrintWriter(System.out);
    static Scanner sc = new Scanner(System.in);
    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    public static void main(String[] args) throws IOException {
        Main main = new Main();
        String ans = main.solve();
        System.out.println(ans);
    }
    String solve() throws IOException{
        String line = reader.readLine();
        int n;
        try{
            n = Integer.parseInt(line);
            Pair[] list = new Pair[n];
            for(int i=0;i<n;i++){
                String s = reader.readLine();
                int[] temp = helper(s,i);
                list[i] = new Pair(temp[0], temp[1]);
            }
            Arrays.sort(list);
            int left = 0;
            for(Pair e:list){
                if(left+e.mini<0) return "No";
                left += e.left;
            }
            return left==0?"Yes":"No";
        } catch (Exception e){
            System.out.println(line);
            return "err";
        }

    }
    int[] helper(String s, int idx){
        int left = 0, mini = 100;
        for(char c:s.toCharArray()){
            if(c=='(') left++;
            else left--;
            mini = Math.min(mini,left);
        }
        return new int[]{left, mini, idx};
    }
    class Pair implements Comparable<Pair>{
        int left,mini;
        public Pair(int le, int mi){
            left = le; mini = mi;
        }
        public int compareTo(Pair p){
//            int res1 = Math.min(this.mini, this.left+p.mini);
            int res1 = this.mini<this.left+p.mini?this.mini:this.left+p.mini;
//            int res2 = Math.min(p.mini, this.mini+p.left);
            int res2 = p.mini < this.mini+p.left? p.mini:this.mini+p.left;
            if(res1 == res2) return 0;
            return res1 < res2? 1:-1;
        }
    }
}