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 = list(input() for _ in range(N))
X = []
for s in S:
    l,r = 0,0
    for c in s:
        if c == ")":
            if r > 0:
                r -= 1
            else:
                l += 1
        else:
            r += 1
    X.append([l,r])
X.sort(key = lambda x:x[0])
Y = []
L = 0
for p,q in X:
    if p > L:
        print("No")
        quit()
    if q >= p:
        L -= p
        L += q
    else:
        Y.append([p,q])
Y.sort(key = lambda x:-x[1])
for a,b in Y:
    if a > L:
        print("No")
        quit()
    L -= a
    L += b
if L:
    print("No")
else:
    print("Yes")     