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 heapq import heappush, heappop
import sys
input = sys.stdin.readline

N = int(input())
pos = []
zero = []
neg = []
for _ in range(N):
    S = input().rstrip()
    m = s = 0
    for c in S:
        if c == '(':
            s += 1
        else:
            s -= 1
            m = min(m, s)
    if s > 0:
        heappush(pos, (-m, s)) # take larger mins first
    elif s == 0:
        heappush(zero, (m, s))
    else:
        heappush(neg, (m - s, s)) # take smaller mins first
num = 0
while pos:
    m, s = heappop(pos)
    if num - m < 0:
        print('No')
        exit()
    num += s
while zero:
    m, s = heappop(zero)
    if num + m < 0:
        print('No')
        exit()
while neg:
    m, s = heappop(neg)
    m += s
    if num + m < 0:
        print('No')
        exit()
    num += s
if num == 0:
    print('Yes')
else:
    print('No')

