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())

a = []
b = []
for i in range(n):
    s = input()
    x = 0
    y = 0
    for c in s:
        if c == '(':
            y += 1
        else:
            if y >= 1:
                y -= 1
            else:
                x += 1
    if x < y: a.append([x, abs(x-y)])
    else: b.append([y, abs(x-y)])

def calc(a):
    ret = 0
    for x, y in sorted(a):
        if ret < x: return -1
        ret += y
    return ret
   
res1 = calc(a)
res2 = calc(b)
print("Yes" if res1 >= 0 and res1 == res2 else "No")