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_s = [input() for _ in range(N)]
S_data1 = []
S_data2 = []
for S in S_s:
    life = 0
    A=0
    for c in S:
        if c == '(':
            life += 1
        else:
            if life > 0:
                life -= 1
            else:
                A += 1
    if(A<life):
        S_data1.append(tuple([A,life]))
    else:
        S_data2.append(tuple([A,life]))
S_data1.sort()
S_data2 = sorted(S_data2, key=lambda x:-x[1])
S_data1.extend(S_data2)
S_data = tuple(S_data1)
life = 0
answer = True
for S_datum in S_data:
    life -= S_datum[0]
    if life < 0:
        answer = False
        break
    life += S_datum[1]
else:
    if life != 0:
        answer = False

if answer:
    print("Yes")
else:
    print("No")