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 _ in range(n)]
for i in range(n):
    s[i]=input()
#x=[[0,0] for _ in range(n)]
hp,hm=0,0
p=[]
m=[]
for i in range(n):
    t=s[i]
    lv=0
    mn=0
    for u in t:
        if u == '(':
            lv+=1
        elif u == ')':
            lv-=1
        mn=min(mn,lv)
    #x[i][0],x[i][1]=lv,mn
    if lv>=0:
        p.append([lv,mn])
        hp+=lv
    else:
        lv*=-1
        m.append([lv,mn+lv])
        hm+=lv
if hp!=hm:
    print('No')
    exit()
p.sort(key=lambda x: x[1],reverse=1)
m.sort(key=lambda x: x[1],reverse=1)
h=0
lv,mn=0,0
for a,b in p:
    lv+=a
    mn+=b
    if mn<0:
        print('No')
        exit()
    mn=lv
lv,mn=0,0
for a,b in m:
    lv+=a
    mn+=b
    if mn<0:
        print('No')
        exit()
    mn=lv
print('Yes')

#print(lv,mn)
    
