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())
brackets_plus = []
brackets_minus = []
right = 0
left = 0
for i in range(n):
    s = input()
    cur = 0
    m = 0
    for j in range(len(s)):
        if s[j] == "(":
            left += 1
            cur += 1
        else:
            right += 1
            cur -= 1
            m = min(m,cur)
    if cur >= 0:
        brackets_plus.append((m,cur))
    else:
        brackets_minus.append((m,cur,m-cur))
if right != left:
    print("No")
    exit()
cur = 0
brackets_plus.sort(reverse = True)
for i in brackets_plus:
    if i[0] + cur < 0:
        print("No")
        exit()
    cur += i[1]
brackets_minus.sort(key = lambda x:x[2])
for i in brackets_minus:
    if i[0] + cur < 0:
        print("No")
        exit()
    cur += i[1]
print("Yes")