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
# coding: utf-8
import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

# (と)の数は同じ、最下点に注目
N = ir()
S = [[1 if x == '(' else -1 for x in list(sr())] for _ in range(N)]
pos = []
neg = []
for s in S:
    temp = 0
    mi = 0
    for x in s:
        temp += x
        if temp < mi:
            mi = temp
    if temp >= 0:
        pos.append((mi, temp))
    else:
        neg.append((mi-temp, -temp))

pos.sort(reverse=True)
neg.sort(reverse=True)
cur_p = 0; cur_n = 0
bl = True
for m, p in pos:
    if cur_p + m < 0:
        bl = False
    cur_p += p

for m, n in neg:
    if cur_n + m < 0:
        bl = False
    cur_n += n

if cur_p != cur_n:
    bl = False

print('Yes' if bl else 'No')
