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 jdk.nashorn.api.scripting.ScriptObjectMirror;

import java.io.*;
import java.util.*;

@SuppressWarnings("unused")
public class Main {
    FastScanner in;
    PrintWriter out;
    final static int MOD = (int)1e9+7;
    final static long INF = Long.MAX_VALUE / 2;
    
    void solve(){
        int N = in.nextInt();
        String[] S = new String[N];
        for(int i = 0; i < N; i++){
            S[i] = in.nextStr();
        }
        
        int MAX = (int)1e6;
        ArrayList<ArrayList<Integer>> list = new ArrayList<>();
        for(int i = 0; i <= MAX; i++) list.add(new ArrayList<>());
        for(int i = 0; i < N; i++){
            int min = 0, d = 0;
            for(int j = 0; j < S[i].length(); j++){
                if(S[i].charAt(j) == '(') d++;
                else d--;
                min = Math.min(min, d);
            }
            list.get(-min).add(d);
        }
        for(int i = 0; i <= MAX; i++) Collections.sort(list.get(i), Collections.reverseOrder());
        int[] idx = new int[MAX+1];
        
        SegmentTreeIndex tree = new SegmentTreeIndex(MAX+1);
        for(int i = 0; i <= MAX; i++){
            if(idx[i] < list.get(i).size()){
                tree.setPoint(i, list.get(i).get(idx[i]));
                idx[i]++;
            }
        }
        
        long MINF = Long.MIN_VALUE / 2;
        int now = 0;
        boolean isOk = true;
        for(int i = 0; i < N; i++){
            int idxM = tree.getSegmentIndex(0, Math.min(now, MAX) + 1);
            long v = tree.getPoint(idxM);
            if(v == MINF){
                isOk = false;
                break;
            }else{
                now += (int)v;
                if(now < 0){
                    isOk = false;
                    break;
                }
                if(idx[idxM] < list.get(idxM).size()){
                    tree.setPoint(idxM, list.get(idxM).get(idx[idxM]));
                    idx[idxM]++;
                }else{
                    tree.setPoint(idxM, MINF);
                }
            }
        }
        if(now != 0) isOk = false;
        out.println(isOk ? "Yes" : "No");
    }
    
    class SegmentTreeIndex{
        int d;
        int[] node;
        long[] arr;
        
        /*二項演算で使える単位元*/
        private long e = Long.MIN_VALUE / 2;
        
        /*要素同士の二項演算、返すのはインデックス*/
        private int f(int e1, int e2){
            return (arr[e1] == arr[e2] ? Math.max(e1, e2) : (arr[e1] > arr[e2] ? e1 : e2));
        }
        
        /*要素更新用の演算(可換でなくてもよい)*/
        private long g(long arrVal, long val){
            return val; //更新
        }
        
        /* 単位元で初期化 */
        public SegmentTreeIndex(int sz){
            long[] v = new long[sz];
            Arrays.fill(v, e);
            init(v);
        }
        
        /* 配列vで初期化 */
        public SegmentTreeIndex(long[] v){
            init(v);
        }
        
        private void init(long[] v){
            d = 1;
            while(d < v.length) d *= 2;
            arr = new long[v.length];
            node = new int[2*d];
            for(int i = 0; i < v.length; i++) {
                arr[i] = v[i];
                node[i+d] = i;
            }
            for(int i = d-1; i > 0; i--)
                node[i] = f(node[2*i], node[2*i+1]);
        }
        
        public long getPoint(int x){
            return arr[x];
        }
        
        /* 0-indexed:xの要素をg(node[x], val)に更新 */
        public void setPoint(int x, long val){
            arr[x] = g(arr[x], val);
            x += d;
            while(x > 1){
                x = x / 2;
                node[x] = f(node[2*x], node[2*x+1]);
            }
        }
        
        /* 指定した区間[L,R)の区間演算の結果を求めるクエリ */
        public int getSegmentIndex(int L, int R){
            L += d;
            R += d;
            int resL = node[L], resR = node[R-1];
            while (L < R) {
                if ((L & 1) != 0){
                    resL = f(resL, node[L]);
                    L++;
                }
                if ((R & 1) != 0){
                    --R;
                    resR = f(resR, node[R]);
                }
                L >>= 1;
                R >>= 1;
            }
            return f(resL, resR);
        }
    }
    
    public static void main(String[] args) {
        new Main().m();
    }
    
    private void m() {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        /*
        try {
            String path = "input.txt";
            out = new PrintWriter(new BufferedWriter(new FileWriter(new File(path))));
        }catch (IOException e){
            e.printStackTrace();
        }
        */
        solve();
        out.flush();
        in.close();
        out.close();
    }
    
    static class FastScanner {
        private Reader input;
        
        public FastScanner() {this(System.in);}
        public FastScanner(InputStream stream) {this.input = new BufferedReader(new InputStreamReader(stream));}
        public void close() {
            try {
                this.input.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        
        public int nextInt() {return (int) nextLong();}
        
        public long nextLong() {
            try {
                int sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                long ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) return ret * sign;
                    ret *= 10;
                    ret += b - '0';
                }
            } catch (IOException e) {
                e.printStackTrace();
                return -1;
            }
        }
        
        public double nextDouble() {
            try {
                double sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                double ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) break;
                    ret *= 10;
                    ret += b - '0';
                }
                if (b != '.') return sign * ret;
                double div = 1;
                b = input.read();
                while ('0' <= b && b <= '9') {
                    ret *= 10;
                    ret += b - '0';
                    div *= 10;
                    b = input.read();
                }
                return sign * ret / div;
            } catch (IOException e) {
                e.printStackTrace();
                return Double.NaN;
            }
        }
        
        public char nextChar() {
            try {
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                return (char) b;
            } catch (IOException e) {
                e.printStackTrace();
                return 0;
            }
        }
        
        public String nextStr() {
            try {
                StringBuilder sb = new StringBuilder();
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                while (b != -1 && !Character.isWhitespace(b)) {
                    sb.append((char) b);
                    b = input.read();
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }
        
        public String nextLine() {
            try {
                StringBuilder sb = new StringBuilder();
                int b = input.read();
                while (b != -1 && b != '\n') {
                    sb.append((char) b);
                    b = input.read();
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }
        
        public int[] nextIntArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }
        
        public int[] nextIntArrayDec(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt() - 1;
            }
            return res;
        }
        
        public int[] nextIntArray1Index(int n) {
            int[] res = new int[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextInt();
            }
            return res;
        }
        
        public long[] nextLongArray(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }
        
        public long[] nextLongArrayDec(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong() - 1;
            }
            return res;
        }
        
        public long[] nextLongArray1Index(int n) {
            long[] res = new long[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextLong();
            }
            return res;
        }
        
        public double[] nextDoubleArray(int n) {
            double[] res = new double[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextDouble();
            }
            return res;
        }
    }
}