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())

pdat=[]
mdat=[]

for i in range(n):
    s=input()
    
    mini=0
    now=0
    for q in range(len(s)):
        if s[q]=="(":
            now+=1
        else:
            now-=1
            mini=(min(mini,now))
    if now>=0:
        pdat.append((now,mini,mini-now))
    else:
        mdat.append((now,mini,mini-now))

pdat.sort(key=lambda x:-x[1])
mdat.sort(key=lambda x:x[2])

now=0
for d in pdat+mdat:
    if now+d[1]<0:
        print("No")
        break
    now+=d[0]
else:
    if now==0:
        print("Yes")
    else:
        print("No")