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
import sys
readline = sys.stdin.readline

N = int(readline())
S = [readline().strip() for i in range(N)]

D = []
L, R = [], []
for s in S:
    l, r = 0, 0
    for c in s:
        if c == ')':
            if l > 0:
                l -= 1
            else:
                r += 1
        else:
            l += 1
    if l == 0 and r == 0:
        pass
    elif l == 0:
        R.append(r)
    elif r == 0:
        L.append(l)
    else:
        D.append((l, r))

L = sum(L)
R = sum(R)

inc = []
dec = []
for l, r in D:
    if l > r:
        inc.append((l, r))
    else:
        dec.append((l, r))

inc.sort(key=lambda x:x[1])
dec.sort(key=lambda x:-x[1])

D = inc + dec

for i, (l,r) in enumerate(D):
    L -= r
    if L < 0:
        print('No')
        exit(0)
    L += l

if L == R:
    print('Yes')
else:
    print('No')
