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
# input
N = int(input())
S = [input() for _ in range(N)]

# process
T = []
for s in S:
    while '()' in s:
        s = s.replace('()', '')
    T.append(s)

l1 = []
l2 = []
for t in T:
    op = t.find('(')
    if op < 0:
        op = len(t)
    cl = len(t) - op
    
    if cl+op != 0:
        if cl <= op:
            l1.append((cl, op))
        else:
            l2.append((op, cl))

l1.sort()
l2.sort(reverse=True)

result = False
x = 0
if len(l1)+len(l2) == 0:
    result = True
elif len(l1)>0 and len(l2)>0 and l1[0][0]+l2[-1][0] == 0:
    for cl, op in l1:
        x -= cl
        if x < 0:
            break
        x += op
    
    if x >= 0:
        for op, cl in l2:
            x -= cl
            if x < 0:
                break
            x += op
            
        if x == 0:
            result = True

# output
print("Yes" if result else "No")
