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
n = int(input())
x, y = [], []
for _i in range(n):
    s = input()
    p = 0
    m = 0
    for j in range(len(s)):
        if s[j]=="(":
            p += 1
        else:
            p -= 1
            m, _m = sorted([p, m])
    if p > 0:
        x.append([m, p])
    else:
        y.append([m-p, -p])

x.sort(reverse=True)
y.sort(reverse=True)
r = 0
for s, t in x:
    if r+s < 0:
        print("No")
        sys.exit()
    r += t
result = 0
for s, t in y:
    if result+s < 0:
        print("No")
        sys.exit()
    result += t
if r-result == 0:
    print("Yes")
else:
    print("No")