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)










def     process(tab, first, end):
    #print(tab)
    #print(first, end)
    total = first
    for i in tab:
        total += i[0]
        if (total < 0):
            return ("No")
    if (total == end):
        return ("Yes")
    return ("No")




N  = int(input())

first = -1
last = -1
clean = 0
tab = []
total = 0
for i in range(N):
    s = input()
    avant = 0
    apres = 0
    for j in s:
        if (j == '('):
            apres += 1
        elif (j == ')'):
            if (apres > 0):
                apres -= 1
            else:
                avant += 1
    if (avant == 0 and apres > 0 and first == -1):
        first = apres
    elif (apres == 0 and avant > 0 and last == -1):
        last = avant
    elif (avant > 0 or apres > 0):
        tab.append((apres - avant, avant, apres, s))
    else:
        clean += 1
    total += avant - apres
if (first == -1 and clean > 0):
    first = 0
    clean -= 1
if (last == -1 and clean > 0):
    last = 0


tab = sorted(tab)
tab = tab[::-1]
if (total == 0 and first > -1 and last > -1):
    res = process(tab, first, last)
else:
    if (total == 0 and N == 1):
        res = "Yes"
    else:
        res = "No"
print(res)