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 = [input() for _ in range(N)]

T = [0]*N
M = [0]*N
for i in range(N):
    res = 0
    idx = 0
    s = S[i]
    l = len(s)
    m = 0
    while idx<l:
        if s[idx]==')':
            res -= 1
            m = min(res,m)
        else:
            res += 1
        idx += 1
    
    M[i] = m
    T[i] = res

Tp = []
Tn = []
for i in range(N):
    if T[i]>=0:
        Tp.append([M[i], T[i]])
    else:
        Tn.append([M[i]-T[i], -T[i]])

Tp.sort(reverse = True)
Tn.sort(reverse = True)
res = 0
for m,t in Tp:
    if res<-m:
        print('No')
        exit()
    res += t

resn = 0
for m,t in Tn:
    if resn<-m:
        print('No')
        exit()
    resn += t
if res==resn:
    print('Yes')
else:
    print('No')