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: Accepted)

import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {

    private static final int MOD = 998244353;

    public Main(FastScanner in, PrintWriter out) {
        int N = in.nextInt();

        Node[] A = new Node[N];
        for (int i = 0; i < N; i++) {
            String s = in.next();
            int l = 0, r = 0;
            for (int j = 0; j < s.length(); j++) {
                char c = s.charAt(j);
                if (c == '(') {
                    l++;
                } else {
                    if (l == 0) r++;
                    else l--;
                }
            }
            A[i] = new Node(l, r);
        }
        Arrays.sort(A, Comparator.comparingInt(a -> a.right));

        PriorityQueue<Node> q = new PriorityQueue<>();
        int left = 0, i = 0;
        while (i < N || !q.isEmpty()) {
            if (i < N && left >= A[i].right) {
                q.add(A[i++]);
            } else if (!q.isEmpty()) {
                Node cur = q.remove();
                int l = cur.left, r = cur.right;
                // out.printf("%d, %d, %d%n", l, r, left);
                if (left < r) {
                    out.println("No");
                    return;
                }
                left = left - r + l;
            } else
                break;
        }
        if (i < N || left > 0) {
            out.println("No");
        } else
            out.println("Yes");
    }

    static class Node implements Comparable<Node> {
        int left;
        int right;
        Node(int l, int r) {
            left = l;
            right = r;
        }

        public int compareTo(Node other) {
            if (this.left == other.left) {
                return Integer.compare(this.right, other.right);
            }
            return Integer.compare(other.left, this.left);
        }
    }

    private int pow(int x, int p) {
        long res = 1, a = x;
        while (p > 0) {
            if (p % 2 == 1)
                res = res * a % MOD;

            a = a * a % MOD;
            p /= 2;
        }
        return (int)res;
    }

    private long gcd(long a, long b) {
        while (true) {
            if (b == 0) return a;
            long tmp = a;
            a = b;
            b = tmp % b;
        }
    }

    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        // Scanner in = new Scanner(
                // new BufferedReader(new InputStreamReader(System.in)));
        FastScanner in = new FastScanner(System.in);

        Main sol = new Main(in, out);

        out.close();
    }
}

// Pair
class Pair<T extends Comparable<? super T>, U extends Comparable<? super U>> implements Comparable<Pair<T, U>> {
    T a;
    U b;
    Pair() { }
    Pair(T a, U b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public String toString() { return "("+a.toString()+", "+b.toString()+")"; }

    @Override
    public int hashCode() { return Objects.hash(a, b); }

    @Override
    public boolean equals(Object obj) {
        if(this == obj) return true;
        if(obj == null) return false;
        if(this.getClass() != obj.getClass()) return false;
        Pair that = (Pair) obj;
        if(this.a.getClass() != that.a.getClass()) return false;
        if(this.b.getClass() != that.b.getClass()) return false;
        if(!this.a.equals(that.a)) return false;
        if(!this.b.equals(that.b)) return false;
        return true;
    }

    @Override
    public int compareTo(Pair<T, U> that) {
        int c = (this.a).compareTo(that.a);
        if(c == 0) c = (this.b).compareTo(that.b);
        return c;
    }
}


class FastScanner{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream)
    {
        this.stream = stream;
    }

    int read()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars){
            curChar = 0;
            try{
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    boolean isSpaceChar(int c)
    {
        return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
    }

    boolean isEndline(int c)
    {
        return c=='\n'||c=='\r'||c==-1;
    }

    int nextInt()
    {
        return Integer.parseInt(next());
    }

    long nextLong()
    {
        return Long.parseLong(next());
    }

    double nextDouble()
    {
        return Double.parseDouble(next());
    }

    String next(){
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isSpaceChar(c));
        return res.toString();
    }

    String nextLine(){
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isEndline(c));
        return res.toString();
    }
}