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())
A=[]
for i in range(n):
    s=input()
    l=0
    o=0
    for c in s:
        if c=='(':
            l+=1
        else:
            l-=1
            o=min(o,l)
    A.append((l,o))
A.sort(key=lambda x:-10**9 if x[1]==0 else -x[1] if x[0]>=0 else 10**7+x[1]-x[0])
last=0
for l,o in A:
    if last+o<0:
        print("No")
        exit(0)
    last+=l
print("Yes" if last==0 else "No")