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
import sys
input=sys.stdin.readline
n=int(input())
sp=[]
sn=[]
for i in range(n):
    s=input().rstrip()
    m=0
    temp=0
    for j in s:
        if j=='(':
            temp+=1
        else:
            temp-=1
        m=min(m,temp)
    m=-m
    if temp>=0:
        sp.append((m,temp))
    else:
        sn.append((m+temp,-temp))
sp.sort()
sn.sort()
vp=0
for i in sp:
    if vp-i[0]<0:
        print('No')
        sys.exit()
    else:
        vp+=i[1]
vn=0
for i in sn:
    if vn-i[0]<0:
        print('No')
        sys.exit()
    else:
        vn+=i[1]
if vp==vn:
    print('Yes')
else:
    print('No')
