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())
X = [input() for _ in range(N)]

ctr = [[], []]
for s in X:
    t = [0] * (len(s) + 1)
    for j in range(len(s)):
        t[j + 1] = t[j] + int(s[j] == "(") - int(s[j] == ")")

    if t[-1] > 0:
        ctr[0].append((min(t), t[-1]))
    else:
        ctr[1].append((min(t) - t[-1], -t[-1]))

flag = True
tmp = 0
for i in range(2):
    cur = 0
    for m, c in sorted(ctr[i], reverse=True):
        flag &= cur + m >= 0
        cur += c

    if i == 0:
        tmp = cur
    else:
        flag &= tmp == cur

if flag:
    print("Yes")
else:
    print("No")
