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())

ls1 = []
ls2 = []

for item in s:
    stk1 = []
    stk2 = []
    for ch in item:
        if ch == '(':
            stk2.append(ch)
        else:
            if len(stk2) > 0:
                stk2.pop()
            else:
                stk1.append(ch)
    l1 = len(stk1)
    l2 = len(stk2)
    if l2 >= l1:
        ls1.append((l1, l2))
    else:
        ls2.append((l1, l2))


ls1.sort()

cnt = 0

for item in ls1:
    cnt -= item[0]
    if cnt < 0:
        print('No')
        exit()
    else:
        cnt += item[1]

ls2.sort(key=lambda x: x[1])
ls2.reverse()

for item in ls2:
    cnt -= item[0]
    if cnt < 0:
        print('No')
        exit()
    else:
        cnt += item[1]

if cnt != 0:
    print('No')
else:
    print('Yes')
