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 CPP):

Solution:
#include <cstdio>

const int N=200005;

int n,a[N],b[N];

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d",a+i);
    for(int i=0;i<n;i++)scanf("%d",b+n-i);
    bool success=true;
    for(int i=1,j,t;i<=n&&success;i++)
        if(a[i]==b[i])
        {
            for(int k=1;k<=n&&a[i]==b[i];k++)
                if(b[k]!=b[i]&&a[k]!=b[i])
                    t=b[i],b[i]=b[k],b[k]=t,i++;
            for(int k=1;k<=n;k++)
                if(a[i]==b[i])
                {
                    success=false;
                    break;
                }
        }
    puts(success?"Yes":"No");
    if(success)for(int i=1;i<=n;i++)printf("%d ",b[i]);
    return 0;
}