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())
pos=[]
neg=[]
for i in range(n):
    s=input()
    bal=0
    mn=0
    for ch in s:
        if ch=='(':
            bal+=1
        if ch==')':
            bal-=1
        mn=min(mn,bal)
    if -mn<bal-mn:
        pos.append((-mn,bal-mn))
    else:
        neg.append((-mn,bal-mn))
def cmp(it):
    return -it[1]
pos.sort()
neg.sort(key=cmp)
bal=0
ok=True
for (m,b) in pos:
    if bal-m<0:
        ok=False
    bal+=b-m
for (m,b) in neg:
    if bal-m<0:
        ok=False
    bal+=b-m
if bal!=0:
    ok=False
if ok:
    print("Yes")
else:
    print("No")