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 itertools import permutations
n = int(input())
s = [input() for i in range(n)]
lsa=list() #mn,end
lsd=list()
for i in range(n):
    now = 0
    mn = 0
    for c in s[i]:
        if c == '(':
            now += 1
        else:
            now -= 1
            mn = min(mn,now)
    if now >= 0:
        lsa.append([mn,now])
    else:
        lsd.append([mn-now,-now])

lsa.sort(reverse=True)
tmn = 0
tend = 0
flag=True
# ascent
for mn,end in lsa:
    tmn = mn + tend
    tend += end
    if tmn < 0 or tend < 0:
        flag = False
        break
tenda = tend

# descent
lsd.sort(reverse=True)
tmn = 0
tend = 0

for mn,end in lsd:
    tmn = mn + tend
    tend += end
    if tmn < 0 or tend < 0:
        flag=False
        break

if flag and tend == tenda:
    print("Yes")
else:
    print("No")



