A bracket sequence is a string that is one of the following:

1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. 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`.

Examples

Input

2
)
(()


Output

Yes


Input

2
)(
()


Output

No


Input

4
((()))
((((((
))))))
()()()


Output

Yes


Input

3
(((
)
)


Output

No
import java.util.*;

public class Main {

    Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {
        int n = sc.nextInt();
        List<Pair> ls = new ArrayList<>();
        List<Pair> rs = new ArrayList<>();

        int total = 0;

        for (int i=0; i<n; i++) {
            char[] arr = sc.next().toCharArray();
            int b = 0;
            int h = 0;
            for (int j=0; j<arr.length; j++) {
                if (arr[j] == '(') {
                    h++;
                } else {
                    h--;
                }
                b = Math.min(b, h);
            }
//            System.out.println(b);
//            System.out.println(h);
            if (0 < h) ls.add(new Pair(b, h));
            else rs.add(new Pair(b-h, -h));
            total += h;
        }

        Collections.sort(ls);
        Collections.sort(rs);

        if (check(ls) && check(rs) && total == 0) {
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }

    }


    boolean check(List<Pair> pairList) {
        int h = 0;
        for (Pair p: pairList) {
            int b = h + p.b;
            if (b < 0) return false;
            h += p.h;
        }
        return true;
    }

    public class Pair implements Comparable<Pair>{
        int b;
        int h;
        public Pair(int b, int h) {
            this.b = b;
            this.h = h;
        }

        public int compareTo(Pair pair) {
            if (this.b < pair.b) return 1;
            if (pair.b < this.b) return -1;
            return 0;
        }

    }
}

