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)]
B1 = []
B2 = []
for s in S:
    ncl = nop = 0
    for c in s:
        if c=='(':
            nop+=1
        else:
            if nop>0: nop-=1
            else: ncl+=1

    if nop-ncl>=0:
        B1.append((nop, ncl))
    else:
        B2.append((nop, ncl))

#print(B)
    
Bl = sorted(B1, key=lambda x:x[1])
Br = sorted(B2, key=lambda x:x[0])

xl = 0
for nop, ncl in Bl:
    if ncl>xl:
        print('No')
        exit()
    xl+=nop-ncl

xr = 0
for nop, ncl in Br:
    if nop>xr:
        print('No')
        exit()
    xr+=ncl-nop

print('Yes' if xl==xr else 'No')