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 count(i, s):
    left = right = 0
    for e in s:
        if e == "(":
            left += 1
        else:
            if left == 0:
                right += 1
            else:
                left -= 1

    return left-right, left, right, i


n = int(input())
S = [input() for i in range(n)]
s1 = []
s2 = []
for i, e in enumerate(S):
    c = count(i, e)
    # print(i, c)
    if c[0] >= 0:
        s1.append((c[2], c[3]))
    else:
        s2.append((-c[1], c[3]))

s1.sort()
s2.sort()
# print(s1, s2)
s = []
for e in s1:
    s.append(S[e[1]])
for e in s2:
    s.append(S[e[1]])
# print(s)

_, left, right, _ = count(0, "".join(s))
if left == right == 0:
    print("Yes")
else:
    print("No")

