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())

mem = [0] * N
for i in range(N):
    s = input()
    x = 0
    y = 0
    for j in range(len(s)):
        if s[j] == '(':
            x += 1
        else:
            x -= 1
            y = min(x, y)
    mem[i] = (x, y)

mem_a = sorted([ele for ele in mem if ele[0] > 0], key=lambda x: -x[1])
mem_b = sorted([ele for ele in mem if ele[0] <= 0], key=lambda x: x[1]-x[0])

ans = True
val = 0
for ele in mem_a:
    if val + ele[1] < 0:
        ans = False
    val += ele[0]
for ele in mem_b:
    if val + ele[1] < 0:
        ans = False
    val += ele[0]


YesNo = lambda tf: print('Yes') if tf else print('No')
YesNo(ans and val == 0)