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 = []
for i in range(n):
    a = input()
    b = []
    for j in range(len(a)):
        if a[j]=='(':
            b.append(1)
        else:
            b.append(-1)
    s.append(b)

l = []
r = []
for x in s:
    b = 0
    c = 0
    for y in x:
        c+=y
        b = min(b,c)
    z = len(x)
    d = 0
    e = 0
    for j in range(z):
        e += x[z-j-1]
        d = max(d,e)
    if c>0:
        l.append([b,c])
    else:
        r.append([d,c])
l.sort(reverse=True)
r.sort()

flag = 1
x = 0
for b,c in l:
    if x+b<0:
        flag = 0
    x += c

y = 0
for d,c in r:
    if y+d>0:
        flag = 0
    y += c

if y+x!=0:
    flag = 0
print('Yes' if flag else'No')





