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

from functools import reduce
n, *s = open(0).read().split()
u = []
for t in s:
    close_cnt = 0
    tmp = 0
    for c in t:
        tmp += (1 if c == '(' else -1)
        close_cnt = min(close_cnt, tmp)
    u.append((close_cnt, tmp - close_cnt))
M = 10**6 + 1
acc = 0
for a, b in sorted([x for x in u if sum(x) >= 0], key=lambda z: -z[0]):
    if acc + a < 0:
        print("No")
        exit(0)
    else:
        acc += a + b
for a, b in sorted([x for x in u if sum(x) < 0], key=lambda z: -z[1]):
    if acc + a < 0:
        print("No")
        exit(0)
    else:
        acc += a + b
print(("No" if acc else "Yes"))