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
def Yes():
    print('Yes')
    exit()


def No():
    print('No')
    exit()


def parse(s):
    ret = [0, 0]
    for c in s:
        if c == ')':
            if ret[0]:
                ret[0] -= 1
            else:
                ret[1] -= 1
        else:
            ret[0] += 1
    return ret


N = int(input())
S = [parse(input()) for _ in range(N)]
S.sort(key=lambda a: -a[0] - a[1])
S1 = []
S2 = []
for s in S:
    if s[0] + s[1] >= 0:
        S1 += [s]
    else:
        S2 += [s]
S1.sort(key=lambda a: -a[1])
S2.sort(key=lambda a: -a[0])
cnt = 0
for s in S1:
    cnt += s[1]
    if cnt < 0:
        No()
    cnt += s[0]
for s in S2:
    cnt += s[1]
    if cnt < 0:
        No()
    cnt += s[0]
if cnt:
    No()
Yes()
