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 sys
n = int(input())
si = []
for _ in range(n):
    s = input()
    l = 0
    r = 0
    count = 0
    for i in range(len(s)):
        if s[i] == "(":
            count += 1
        else:
            count = max(0, count-1)
    l = count
    count = 0
    for i in range(len(s)-1, -1, -1):
        if s[i] == ")":
            count += 1
        else:
            count = max(0, count-1)
    r = count
    si.append((l, r))

if len(si) == 1:
    if si[0] == (0, 0):
        print("Yes")
        sys.exit()

index_l = -1
index_r = -1
maxi_l = 0
maxi_r = 0
for i in range(n):
    a, b = si[i]
    if a == 0:
        if maxi_l < b:
            maxi_l = b
            index_l = i
    if b == 0:
        if maxi_r < a:
            maxi_r = a
            index_r = i

if index_l == -1 or index_r == -1:
    print("No")
    sys.exit()

count = 0
if index_r < index_l:
    count += si.pop(index_l)[1]
    last = si.pop(index_r)
else:
    last = si.pop(index_r)
    count += si.pop(index_l)[1]

minus = []
plus = []
while si:
    a, b = si.pop()
    if a <= b:
        plus.append((a, b))
    else:
        minus.append((a, b))

plus.sort()
minus.sort(reverse = True)

for a, b in plus:
    if count >= a:
        count += b-a
    else:
        print("No")
        sys.exit()
for a, b in minus:
    if count >= a:
        count += b-a
    else:
        print("No")
        sys.exit()

count -= last[0]

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