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 Python (3.8.2) (judge verdict: Wrong Answer)

# coding: utf-8
import sys
from operator import itemgetter
sysread = sys.stdin.readline
read = sys.stdin.read
from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
#from itertools import combinations, product
#import bisect# lower_bound etc
#import numpy as np
#import queue# queue,get(), queue.put()
def run():
    N = int(input())
    current = 0
    ways = []
    dic = {'(': 1, ')': -1}
    for _ in range(N):
        S = input()
        go = 0
        max_depth = 0
        for s in S:
            go += dic[s]
            max_depth = min(max_depth, go)
        if current + max_depth < 0:
            ways.append((go, max_depth))
        else:
            current += go


    ways = sorted(ways, key=lambda x:x[0], reverse=True)

    while ways:
        done = False
        for idx, (go, max_depth) in enumerate(ways):
            if current + max_depth >= 0:
                if go < 0:
                    break
                current += go
                del ways[idx]
                done = True
        if not done:
            break

    ways = [(-a, b) for a, b in ways]
    ways = sorted(ways, key = itemgetter(1,0))

    while ways and current >= 0:
        done = False
        for idx, (go, max_depth) in enumerate(ways):
            if go <= 0:
                print('No')
                return None
            if current + max_depth >= 0:
                current -= go
                del ways[idx]
                done = True
                break
        if not done:
            print('No')
            return None


    if current == 0:
        print('Yes')
    else:
        print('No')

if __name__ == "__main__":
    run()