A bracket sequence is a string that is one of the following:

1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. 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`.

Examples

Input

2
)
(()


Output

Yes


Input

2
)(
()


Output

No


Input

4
((()))
((((((
))))))
()()()


Output

Yes


Input

3
(((
)
)


Output

No
N = int(input())
S = [input() for i in range(N)]

LR = []
for s in S:
    left, right = 0, 0
    for ss in s:
        if ss == "(":
            left += 1
        else:
            if left:
                left -= 1
            else:
                right += 1
    LR.append([left, right])
#print(LR)

plus = []
minus = []
for l, r in LR:
    if l >= r:
        plus.append([l, r])
    else:
        minus.append([l, r])
        
plus.sort(key = lambda x: x[1])
minus.sort(key = lambda x: -x[0])

cnt = 0
for l, r in plus + minus:
    cnt -= r
    if cnt < 0:
        print("No")
        exit()
    cnt += l
        
if cnt == 0:
    print("Yes")
else:
    print("No")