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
def score(a,b):
    if b-a >= 0:
        return a
    else:
        return 10**6+1-b

N = int(input())

A = [0]*N
B = [0]*N

for i in range(N):
    S = input()
    a = 0
    b = 0
    for j in range(len(S)):
        if S[j] == ')':
            a += 1
        else:
            a -= 1
        A[i] = max(A[i],a)

        if S[-j-1] == '(':
            b += 1
        else:
            b -= 1
        B[i] = max(B[i],b)

#print('S',S)
#print('A',A)
#print('B',B)

L = sorted(list(range(N)),key = lambda i:score(A[i],B[i]))

SA = 0
SB = 0

#print('L',L)

for i in range(N):
    if SB > A[L[i]]:
        SB += B[L[i]] - A[L[i]]
    else:
        SA += A[L[i]]-SB
        SB = B[L[i]]
    #print(SA,SB)

if SA == 0 and SB == 0:
    print('Yes')
else:
    print('No')