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())
d=[]
e=[]
for i in range(n):
    p=[0,0]
    s=input()
    for j in s:
        if j==")":
            if p[0]!=0:
                p[0]-=1
            else:
                p[1]+=1
        else:
            p[0]+=1
    if p[0]-p[1]>=0:
        d.append(p)
    else:
        e.append(p)
d=sorted(d,key=lambda x:x[1])
e=sorted(e,key=lambda x:-x[0])
s=d+e
q=0
for i,j in s:
    if q<j:
        print("No")
        exit()
    else:
        q=q-j+i
if q==0:
    print("Yes")
else:
    print("No")
