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
from bisect import bisect
N = int(input())
S = [input() for _ in range(N)]

def count(s):
    n = len(s)
    n1 = 0
    n2 = 0
    for i in range(n):
        if s[i]=='(':
            n2 += 1
        else:
            if n2 > 0:
                n2 -= 1
            else:
                n1 += 1
    return n1,n2

l1 = []
l2 = []
m1 = 0
m2 = 0
for i in range(N):
    n1,n2 = count(S[i])
    if n1+n2==0:
        continue
    if n1 == 0:
        m1 += n2
        continue
    if n2 == 0:
        m2 += n1
        continue
    if n2-n1>=0:
        l1.append([n1,n2])
    else:
        l2.append([n1,n2])

ans = 'Yes'
l1.sort()
for i in range(len(l1)):
    n1,n2 = l1[i]
    if m1 < n1:
        ans = 'No'
        break
    m1 += n2-n1

l2.sort(key=lambda x:x[1])
for i in range(len(l2)):
    n1,n2 = l2[i]
    if m2 < n2:
        ans = 'No'
        break
    m2 += n1-n2

if m1!=m2:
    ans = 'No'

print(ans)

