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
n=int(input())
s=[input() for _ in range(n)]
d0={}
d1={}
ma=0
mab=0
for si in s:
    a,b=0,0
    for x in si:
        if x=='(':
            b+=1
        else:
            b-=1
        a=min(b,a)
    a=-a
    if b>=0:
        if a in d0:
            d0[a].append([a,b])
        else:
            d0[a]=[[a,b]]
        ma=max(ma,a)
    else:
        if a+b in d1:
            d1[a+b].append([a,b])
        else:
            d1[a+b]=[[a,b]]
        mab=max(mab,a+b)
now=0
for i in range(ma+1):
    if i not in d0:continue
    if now>=i:
        for a,b in d0[i]:
            now+=b
    else:
        print('No')
        exit()
for i in range(mab,-1,-1):
    if i not in d1:continue
    for a,b in d1[i]:
        if now>=a:
            now+=b
        else:
            print('No')
            exit()
if now==0:
    print('Yes')
else:
    print('No')