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)

from sys import stdin
import sys
import math
from functools import reduce
import functools
import itertools
from collections import deque,Counter,defaultdict
from operator import mul
import copy
# ! /usr/bin/env python
# -*- coding: utf-8 -*-
import heapq
sys.setrecursionlimit(10**6)
INF =  float("inf")
import bisect

def count(s):
    a = 0
    aa = 0
    b = 0
    bb = 0
    for i in range(len(s)):
        if s[i] == ")":
            if aa == 0:
                a = a + 1
            else:
                aa = aa - 1
        if s[i] == "(":
            aa = aa + 1
        if s[len(s)-1-i] == "(":
            if bb == 0:
                b = b + 1
            else:
                bb = bb - 1
        if s[len(s)-1-i] == ")":
            bb = bb + 1
    return [a, b]

N = int(input())

c = []
d = []
for i in range(N):
    s = input()
    e = count(s)
    if e[1] - e[0] >= 0: c.append(e)
    if e[0] - e[1] > 0: d.append(e)

c.sort(key=lambda x: x[0])
d.sort(key=lambda x: x[0])

c = c + d

f = 0
for cc in c:
    f = f - cc[0]
    if f < 0:
        print("No")
        sys.exit()
    f = f + cc[1]

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