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 i in range(N):
    s.append(input())
inc = []
dec = []
total = 0
for i in s:
    cn = 0
    mn = 0
    for j in i:
        if j=="(":
            cn+=1
        else:
            cn-=1
        mn = min(cn,mn)
    total += cn
    if cn>=0:
        inc.append([mn,cn])
    else:
        dec.append([mn-cn,-cn])

inc.sort(reverse=True,key=lambda x:x[0])
dec.sort(reverse=True,key=lambda x:x[0])

def check(lis):
    hi = 0
    for i in lis:
        if hi+i[0]<0:
            return False
        else:
            hi+=i[1]
    return True

if check(inc) and check(dec) and total==0:
    print("Yes")
else:
    print("No")
