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())
s = []
for _ in range(n):
    s.append(input())
a = []
b = []
c = []
for i in s:
    mi = 0
    tmp = 0
    for j in i:
        if j=='(':
            tmp += 1
        else:
            tmp -= 1
        if tmp<mi:
            mi = tmp
    if tmp>0:
        a.append((mi, tmp))
    elif tmp==0:
        b.append((mi, tmp))
    else:
        c.append((mi, tmp))
a.sort(key=lambda x:-x[0])
c.sort(key=lambda x:x[0]-x[1])
tmp = 0
for i, j in a+b+c:
    if tmp+i<0:
        print('No')
        break
    tmp += j
else:
    if tmp==0:
        print('Yes')
    else:
        print('No')