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
import sys
input = sys.stdin.readline

N = int(input())
S = [input()[:-1] for _ in range(N)]
high = []
low = []
for i in range(N):
    cnt = 0
    m = 0
    for j in range(len(S[i])):
        if S[i][j] == "(":
            cnt += 1
        else:
            cnt -= 1
        m = min(m, cnt)
    if cnt > 0:
        high.append([m, cnt])
    else:
        low.append([m-cnt, -cnt])
high.sort(reverse=True)
low.sort(reverse=True)

h = 0
for m, up in high:
    if h+m < 0:
        print("No")
        sys.exit()
    h += up
p = 0
for m, down in low:
    if p+m < 0:
        print("No")
        sys.exit()
    p += down
if h == p:
    print("Yes")
else:
    print("No")


