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
def encode(s):
    val = 0
    min_val = 0
    for c in s:
        if c == '(':
            val += 1
        else:
            val -= 1
            min_val = min(min_val, val)
    return [min_val, val]

def check(s):
    h = 0
    for p in s:
        b = h + p[0]
        if b < 0:
            return False
        h += p[1]
    return True


n = int(input())
ls = []
rs = []
l_total = 0
r_total = 0
for _ in range(n):
    si = encode(input())
    if si[1] > 0:
        ls.append(si)
        l_total += si[1]
    else:
        si[0] -= si[1]
        si[1] *= -1
        rs.append(si)
        r_total += si[1]
list.sort(ls, reverse=True)
list.sort(rs, reverse=True)
if check(ls) and check(rs) and l_total == r_total:
    print("Yes")
else:
    print("No")
