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 <bits/stdc++.h>
using namespace std;
int main() {
    int n;
    cin>>n;
    vector<int> v1(n);
    vector<int> v2(n);
    for(int i=0;i<n;i++){
        cin>>v1[i];
    }
    for(int i=0;i<n;i++){
        cin>>v2[i];
    }
    reverse(v2.begin(),v2.end());
    int c=-1;
    int l=0;
    int r=0;
    for(int i=0;i<n;i++){
        if(v1[i]==v2[i]){
          c=v1[i];
          l=i;
          break;
        }
    }
    for(int i=n-1;i>=0;i--){
         if(v1[i]==v2[i]){
           r=i;
           break;
        }
    }
    for(int i=0;i<n;i++){
       if(v1[i]!=c && v2[i]!=c && l<=r){
           swap(v2[i],v2[l]);
           l++;
       }
    }
    if(l<=r){
        cout<<"No"<<endl;
    }
    else{
        cout<<"Yes"<<endl;
         for(int i=0;i<n;i++){
            cout<<v2[i]<<" ";
        }
    }


}