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()
    l = len(s)
    a=0
    b=0
    a1=0
    b1=0
    for j in range(l):
        if s[j]==')':
            a1+=1
        else:
            a1-=1
        a=max(a1,a)
    for j in range(l):
        if s[l-1-j]=='(':
            b1+=1
        else:
            b1-=1
        b = max(b1,b)
    if a>b:
        right.append((a,b))
    else:
        left.append((a,b))
right.sort(key = lambda x:x[1],reverse=True)
left.sort(key = lambda x:x[0])
all = left+right

if all[0][0]>0:
    print('No')
    exit()
st = all[0][1]
for i in range(1,n):
    st-=all[i][0]
    if st<0:
        print('No')
        exit()
    st+=all[i][1]
if st>0:
    print('No')
else:
    print('Yes')
