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
# F - Bracket Sequencing

from itertools import chain

n = int(input())
ss = [input() for i in range(n)]

def parse(s):
    "バランスしていない閉じ括弧数, 開き括弧数"
    cl, op = 0, 0
    for c in s:
        if c == '(':
            op += 1
        elif op > 0:
            op -= 1
        else:
            cl += 1
    return (cl, op)

inc   = []  # 開き括弧が多い
dec   = []  # 閉じ括弧が多い
close = []  # 閉じ括弧のみ
for s in ss:
    cl, op = parse(s)
    if cl < op:
        inc.append((cl, op))
    elif op == 0:
        close.append((cl, op))
    else:
        dec.append((cl, op))
peak = 0
inc.sort()
dec.sort(reverse=True)
for cl, op in chain(inc, dec, close):
    if peak < cl:
        print('No')
        exit()
    peak += op - cl
print('Yes' if peak == 0 else 'No')
