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: Accepted)

#from collections import deque,defaultdict
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7
#R = 998244353

def ddprint(x):
  if DBG:
    print(x)

n = inn()
ls = []
rs = []
z = 0
for i in range(n):
    ss = ins()
    l = r = 0
    for c in ss:
        if c=='(':
             l += 1
        else:
            if l>0:
                l -= 1
            else:
                r += 1
    rr = r
    l = r = 0
    for j in range(len(ss)-1,-1,-1):
        c = ss[j]
        if c==')':
             r += 1
        else:
            if r>0:
                r -= 1
            else:
                l += 1
    r = rr
    if l>r:
        ls.append((r,l-r))
    elif l<r:
        rs.append((l,r-l))
    else:
        z = max(z,r)
ls.sort()
rs.sort()
#ddprint(ls)
#ddprint(rs)
#ddprint(z)
l = r = 0
for rr,ll in ls:
    if l<rr:
        print('No')
        exit()
    l = l+ll
for ll,rr in rs:
    if r<ll:
        print('No')
        exit()
    r = r+rr
print('Yes' if l==r>=z else 'No')