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, *S = open(0)

L = [s.count("(") for s in S]
R = [s.count(")") for s in S]

X = sorted(((s[:-1], r) for s, l, r in zip(S, L, R) if l - r >= 0), key=lambda x: x[1])
Y = sorted(((s[:-1], l) for s, l, r in zip(S, L, R) if l - r < 0), key=lambda x: -x[1])

cnt = 0
for s, _ in X + Y:
    for si in s:
        cnt += 1 if si == "(" else -1
        if cnt < 0:
            print("No")
            quit()

if cnt == 0:
    print("Yes")
else:
    print("No")