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=[0]*n
info=[0]*n
for i in range(n):
    ss=list(input())
    now=0
    mi=0
    for sss in ss:
        if sss=="(":
            now+=1
        else:
            now-=1
            mi=min(mi,now)
    info[i]=(mi,now)
#info.sort(key=lambda x:(x[1]>=0)*2+(x[0]>=0),reverse=True )

info0 = []
info1 = []
for i,inf in enumerate(info):
    if inf[1]>=0:
        info0.append(inf)
    else:
        info1.append(inf)
info0.sort(key=lambda x:x[0],reverse=True)
info1.sort(key=lambda x:x[1]-x[0],reverse=True)


ans=True
now=0
for inf in info0:
    if now+inf[0]>=0:
        now+=inf[1]
    else:
        ans=False
for inf in info1:
    if now+inf[0]>=0:
        now+=inf[1]
    else:
        ans=False
if now!=0:
    ans=False
    
print(ans*"Yes"+(1-ans)*"No")