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 = [input() for i in range(n)]
ruiseki = [[None] * (len(s[i]) + 1) for i in range(n)]

for i in range(n):
    ruiseki[i][0] = 0
    for j, char in enumerate(s[i]):
        if char == "(":
            ruiseki[i][j + 1] = ruiseki[i][j] + 1
        else:
            ruiseki[i][j + 1] = ruiseki[i][j] - 1


first = []
second = []
now_m = 0
now_s = 0
for i in range(n):
    min_, sum_ = min(ruiseki[i]), ruiseki[i][-1]
    if sum_ > 0:
        first.append((min_, sum_))
    else:
        second.append((min_, sum_))

now_m = 0
now_s = 0

first = sorted(first, reverse=True)
for mi, su in first:
    if now_s + mi < 0:
        print("No")
        exit()
    now_s += su

second = sorted(second, key=lambda x: x[0] - x[1])
for mi, su in second:
    if now_s + mi < 0:
        print("No")
        exit()
    now_s += su

if now_s == 0:
    print("Yes")
else:
    print("No")