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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import bisect
import copy
import heapq
import math
import sys
from collections import *
from itertools import accumulate, combinations, permutations, product
from math import gcd
def input():
    return sys.stdin.readline()[:-1]
def ruiseki(lst):
    return [0]+list(accumulate(lst))
mod=pow(10,9)+7
al=[chr(ord('a') + i) for i in range(26)]
direction=[[1,0],[0,1],[-1,0],[0,-1]]

n=int(input())
s=[input() for i in range(n)]
# lst=[[0]*2 for i in range(n)]

sei=[]
hu=[]

for i in range(n):
    l,r=0,0
    for j in range(len(s[i])):
        if s[i][j]==")":
            if r==0:
                l+=1
            else:
                r-=1
        if s[i][j]=="(":
            r+=1
    if r-l>0:
        sei.append([l,r-l])
    else:
        hu.append([l,r-l])

sei.sort(key=lambda x: (x[0],-x[1]))
hu.sort(key=lambda x: -(x[1]-x[0]))
tmp=0

for i in range(len(sei)):
    if tmp-sei[i][0]<0:
        print("No")
        quit()
    tmp+=sei[i][1]

for i in range(len(hu)):
    if tmp-hu[i][0]<0:
        print("No")
        quit()
    tmp+=hu[i][1]

if tmp==0:
    print("Yes")
else:
    print("No")