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;
const int maxn = 2e5 + 10;
int n;
int A[maxn], B[maxn]; 
int main()
{
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) scanf("%d", &A[i]);
	for(int i = n; i; --i) scanf("%d", &B[i]);
	for(int i = 1; i <= n; ++i)
		if(A[i] == B[i])
		{
			bool f = 0; 
			for(int j = 1; j <= n; ++j)
				if(B[j] != A[i] && B[i] != A[j])
				{
					swap(B[i], B[j]);
					f = 1;
					break;
				} 
			if(!f)
			{
				puts("No");
				return 0;
			}
		}
	puts("Yes");
	for(int i = 1; i <= n; ++i) printf("%d ", B[i]);
	return 0;
}