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 sys import exit
from itertools import accumulate,chain
n,*s=open(0).read().split()
t=[2*(i.count("("))-len(i) for i in s]
if sum(t)!=0:
    print("No");exit()
#pypyではinitialだめ
st=[[t_,min(accumulate(s_,lambda a,b: a+(1 if b=="(" else -1),initial=0))] for s_,t_ in zip(s,t)]

now=0
v=list(filter(lambda x:x[0]>=0,st))
w=list(filter(lambda x:x[0]<0,st))
v.sort(reverse=True,key=lambda z:z[1])
w.sort(key=lambda z:z[0]-z[1],reverse=True)

for sub in chain(v,w):
    if now+sub[1]<0:
        print("No");exit()
    now+=sub[0]
print("Yes")
