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())
left = []
right = []
for i in range(n):
    s = input()
    n0 = 0
    n1 = 0
    l = len(s)
    for j in range(l):
        if s[j] == "(":
            n0 += 1
        else:
            if n0 == 0:
                n1 += 1
            else:
                n0 -= 1
    if n0 > 0 or n1 > 0:
        if n0 >= n1:
            left.append([n1, n0])
        else:
            right.append([n0, n1])
 
left.sort()
right.sort()
 
def solve():
    nl0 = 0
    nl1 = 0
    for p in left:
        if p[0] > nl0:
            return False
        nl0 -= p[0]
        nl0 += p[1]
    nr0 = 0
    nr1 = 0
    for p in right:
        if p[0] > nr1:
            return False
        nr1 -= p[0]
        nr1 += p[1]
    if nl0 == nr1:
        return True
    else:
        return False
 
if solve():
    print("Yes")
else:
    print("No")