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 check(s):
    h = 0
    for p in s:
        b = h + p[0]
        if b < 0:
            return False
        h += p[1]
    return True


N = int(input())
S = []
left = []
right = []
total = 0
for i in range(N):
    last = 0
    bottom = 0
    s = input().strip()
    for c in s:
        if c == "(":
            last += 1
        else:
            last -= 1
        bottom = min(bottom, last)
    if last > 0:
        left.append((bottom, last))
    else:
        right.append((bottom-last, -last))
    total += last

left.sort(key=lambda x: -x[0])
right.sort(key=lambda x: -x[0])

if check(left) and check(right) and total == 0:
    print('Yes')
else:
    print('No')
