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 N = 2e5;
int n, a[N], b[N], t, l, r;

inline void solve() {
	for (register int i = 0; i < n; i++)
		if (a[i] == b[i]) {
			l = i;
			t = a[i];
			break;
		}
	for (register int i = n-1; i >= 0; i--)
		if (a[i] == t && b[i] == t) {
			r = i;
			break;
		}
	for (register int i = 0; i < n; i++)
		if (a[i] != t && b[i] != t && l <= r)
			swap(b[i], b[l++]);
	if (l <= r) {
		puts("No");
		return;
	}
	puts("Yes");
	for (register int i = 0; i < n; i++)
		printf("%d ", b[i]);
	puts("");
}

int main() {
	scanf("%d", &n);
	for (register int i = 0; i < n; i++)
		scanf("%d", a+i);
	for (register int i = n-1; i >= 0; i--)
		scanf("%d", b+i);
	solve();
	return 0;
}