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())
plus=[]
minus=[]
for _ in range(N):
    S=input()
    tmp=0
    min_tmp=0 #)))の
    for i in range(len(S)):
        if S[i]=="(":
            tmp+=1
        else:
            tmp-=1
        if tmp<0:
            min_tmp=min(min_tmp,tmp)
    tmp=0
    max_tmp=0 #(((の
    for i in range(len(S)):
        i=len(S)-i-1
        if S[i]=="(":
            tmp+=1
        else:
            tmp-=1
        if tmp>0:
            max_tmp=max(max_tmp,tmp)
    if tmp>=0:
        plus.append((tmp,max_tmp,-min_tmp))
    else:
        minus.append((tmp,max_tmp,-min_tmp))

plus.sort(key=lambda x:x[2])
minus.sort(reverse=True,key=lambda x:x[1])
ans=0
for i,j,k in plus:
    if ans<k:
        print("No")
        exit()
    ans+=i
for i,j,k in minus:
    if ans<k:
        print("No")
        exit()
    ans+=i
if ans==0:
    print("Yes")
else:
    print("No")
