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 = lambda: sys.stdin.readline().rstrip()
N = int(input())
def I():
    s = input()
    mi = 0
    su = 0
    t = 0
    for a in s:
        if a == "(":
            t += 1
        else:
            t -= 1
            mi = min(mi, t)
    return (mi, t)

X = [I() for _ in range(N)]
if sum([x[1] for x in X]):
    print("No")
    exit()

X = sorted(X, key = lambda x: -10**10 if x[0] == 0 else -10**9 - x[0] if x[1] > 0 else x[0] - x[1])
T = 0
for mi, t in X:
    if T + mi < 0:
        print("No")
        exit()
    T += t
print("Yes")