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;
long long n, k=-1, j=1, a[200005], b[200005]; 
int main(){
       std::ios::sync_with_stdio(false);
	cin>>n;
	for(long long i=1; i<=n; i++)
	cin>>a[i];
	for(long long i=1; i<=n; i++)
	cin>>b[i];
	for(long long i=1; i<=n; i++){
		if(a[i]!=k) j=1;
		if(b[i]==a[i]){
		       for(; j<=n; j++)
		       if(b[j]!=a[i] && a[i]!=a[j]){
		              swap(b[i], b[j]);
		              break;
		       }
		       if(a[i]==b[i]){
		              cout<<"No"<<endl;
		              return 0;
		       }
		}
		k=a[i];
	}
	cout<<"Yes"<<endl;
	for(long long i=1; i<=n; i++)
	cout<<b[i]<<" ";
	cout<<endl;
	return 0;
}