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())
lipp = []
lipm = []
limm = []
allcnt = 0
for _ in range(n):
    s = input()
    cnt = 0
    mi = 0
    for x in s:
        if x == ')':
            cnt -= 1
            mi = min(mi,cnt)
        else:
            cnt += 1
    if mi == 0:
        lipp.append(cnt)
    elif cnt >= 0:
        lipm.append([mi,cnt])
    else:
        limm.append([cnt - mi, mi,cnt])
    allcnt += cnt
if allcnt != 0:
    print('No')
    exit()

now = sum(lipp)
lipm.sort(reverse = True)
limm.sort()

for mi, cnt in lipm:
    if mi + now < 0:
        print('No')
        exit()
    now += cnt

cnt2 = 0
for sa, mi, cnt in limm:
    if sa > cnt2:
        print('No')
        exit()
    cnt2 += -cnt
print("Yes")