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())
sl=0
sr=0
sz=0
lr=[]
rl=[]
for i in range(n):
    s=input()
    l=0
    r=0
    z=0
    for j in s:
        if j=="(":
            l+=1
        else:
            r+=1
        z=max(z,r-l)
    sl+=l
    sr+=r
    if z==0 and l>=r:
        sz+=l-r
    elif l>=r:
        lr.append((z,l-r))
    else:
        rl.append((z,l-r))
if sl!=sr:
    print("No")
    quit()
lr.sort()
for z,i in lr:
    if sz<z:
        print("No")
        quit()
    else:
        sz+=i
rl.sort(key=lambda x:x[0]+x[1] ,reverse=True)
for z,i in rl:
    if sz<z:
        print("No")
        quit()
    else:
        sz+=i
print("Yes")