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 = [input() for _ in range(n)]


def bracket(x):
    # f: final sum of brackets '(':+1, ')': -1
    # m: min value of f
    f = m = 0
    for i in range(len(x)):
        if x[i] == '(':
            f += 1
        else:
            f -= 1
        m = min(m, f)
    # m <= 0
    return f, m


def func(l):
    # l = [(f, m)]
    l.sort(key=lambda x: -x[1])
    v = 0
    for fi, mi in l:
        if v + mi >= 0:
            v += fi
        else:
            return -1
    return v


l1 = []
l2 = []
for i in range(n):
    fi, mi = bracket(s[i])
    if fi >= 0:
        l1.append((fi, mi))
    else:
        l2.append((-fi, mi - fi))

v1 = func(l1)
v2 = func(l2)
if v1 == -1 or v2 == -1:
    ans = 'No'
else:
    ans = 'Yes' if v1 == v2 else 'No'

print(ans)
