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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Objects;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        F solver = new F();
        solver.solve(1, in, out);
        out.close();
    }

    static class F {
        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int N = in.Int();
            List<F.Pair<Integer, Integer>> S = new ArrayList<>();
            long lc = 0, rc = 0;
            for (int i = 0; i < N; i++) {
                String s = in.next();
                String t = null;
                while (true) {
                    t = s.replaceAll("\\(\\)", "");
                    if (s.equals(t)) {
                        break;
                    }
                    s = t;
                }
                if (s.isEmpty()) continue;
                int r = 0, l = 0;
                int len = s.length();
                while (r < len && s.charAt(r) == ')') {
                    r++;
                }
                while (l < len && s.charAt(s.length() - l - 1) == '(') {
                    l++;
                }
                if (l == 0) {
                    rc += r;
                } else if (r == 0) {
                    lc += l;
                } else {
                    S.add(new F.Pair<>(l, r));
                }
            }
            S.sort((o1, o2) -> {
                int c = Integer.compare(o2.k, o1.k);
                if (c == 0) c = Integer.compare(o1.v, o2.v);
                return c;
            });

            if (lc == 0 || rc == 0) {
                out.println("No");
                return;
            }
            long cnt = lc;
            for (F.Pair<Integer, Integer> p : S) {
                cnt -= p.v;
                if (cnt < 0) {
                    out.println("No");
                    return;
                }
                cnt += p.k;
            }
            cnt -= rc;
            out.println(cnt == 0 ? "Yes" : "No");
        }

        static class Pair<K extends Comparable<K>, V extends Comparable<V>> implements Comparable<F.Pair<K, V>> {
            K k;
            V v;

            Pair(K k, V v) {
                this.k = k;
                this.v = v;
            }

            public int compareTo(F.Pair<K, V> o) {
                int c = this.k.compareTo(o.k);
                if (c == 0) c = this.v.compareTo(o.v);
                return c;
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (o == null || getClass() != o.getClass()) return false;
                F.Pair<?, ?> pair = (F.Pair<?, ?>) o;
                return Objects.equals(k, pair.k) &&
                        Objects.equals(v, pair.v);
            }

            public int hashCode() {
                return Objects.hash(k, v);
            }

        }

    }

    static class MyScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public MyScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    return null;
                }
            }
            return st.nextToken();
        }

        public int Int() {
            return Integer.parseInt(next());
        }

    }
}