Problem: Given are two sequences A and B, both of length N. A and B are each sorted in the ascending order. Check if it is possible to reorder the terms of B so that for each i (1 \leq i \leq N) A_i \neq B_i holds, and if it is possible, output any of the reorderings that achieve it.

Constraints

* 1\leq N \leq 2 \times 10^5
* 1\leq A_i,B_i \leq N
* A and B are each sorted in the ascending order.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N


Output

If there exist no reorderings that satisfy the condition, print `No`.

If there exists a reordering that satisfies the condition, print `Yes` on the first line. After that, print a reordering of B on the second line, separating terms with a whitespace.

If there are multiple reorderings that satisfy the condition, you can print any of them.

Examples

Input

6
1 1 1 2 2 3
1 1 1 2 2 3


Output

Yes
2 2 3 1 1 1


Input

3
1 1 2
1 1 3


Output

No


Input

4
1 1 2 3
1 2 3 3


Output

Yes
3 3 1 2

Solution (in PYTHON3):

Solution:
n=int(input())

a=list(map(int,input().split()))
b=list(map(int,input().split()))


b.reverse()
mondai=-1
kasho=0
mondai_basho=-1
for i in range(n):
    if(a[i]==b[i]):
        mondai=a[i]
        kasho+=1
        if(kasho==1):
            mondai_basho=i



kano=True
ans=[]
if(kasho==0):
    ans=b
else:
    hajimea=0
    hajimeb=0
    owaria=0
    owarib=0
    for i in range(n):
        if(a[i]<mondai):
            hajimea+=1
        if(a[i]>mondai):
            owaria+=1
        if(b[i]>mondai):
            hajimeb+=1
        if(b[i]<mondai):
            owarib+=1
    hajime=min(hajimea,hajimeb)
    owari=min(owaria,owarib)
    if(kasho>hajime+owari):
        kano=False
    else:
        for i in range(kasho):
            if(i<hajime):
                temp=b[mondai_basho+i]
                b[mondai_basho+i]=b[i]
                b[i]=temp
            else:
                temp=b[mondai_basho+i]
                b[mondai_basho+i]=b[n-owari+i-hajime]
                b[n-owari+i-hajime]=temp
        ans=b

if(not kano):
    print("No")
else:
    print("Yes")
    for i in range(n):
        b[i]=str(b[i])
    print(" ".join(b))