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, = map(int, input().split())
import sys;input=sys.stdin.readline
X = []
Y = []
for _ in range(N):
    s = input().strip()
    a, b = 0, 0
    for c in s:
        if c == "(":
            a += 1
        else:
            if a > 0:
                a -= 1
            else:
                b += 1
    if a >= b:
        X.append((a, b))
    else:
        Y.append((b, a))
X.sort(key=lambda x:x[1])
Y.sort(key=lambda x:x[1])

s = 0
for i in range(len(X)):
    a, b = X[i]
    if s >= b:
        s += a-b
    else:
        print("No")
        sys.exit()
s2 = 0
for i in range(len(Y)):
    a, b = Y[i]
    if s2 >= b:
        s2 += a-b
    else:
        print("No")
        sys.exit()
if s == s2:
    print("Yes")
else:
    print("No")
