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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

vector<int> a, b;

int main() {
	int n; cin >> n; a.resize(n); b.resize(n);
	for (auto &x : a) { cin >> x; }
	for (auto &x : b) { cin >> x; }
	reverse(b.begin(), b.end()); 
	
	int l = 0, r = 0;
	while (l < n && a[l] != b[l]) { l++; r++; }
	while (r < n && a[r] == b[r]) { r++; }
	for (int i = 0; i < n && l != r; i++)
		if (a[i] != a[l] && b[i] != b[l]) 
			swap(b[l++], b[i]);

	if (l != r) { cout << "No" << '\n'; return 0; }
	cout << "Yes" << '\n';
	for (auto &x : b) cout << x << ' ';
	cout << '\n'; cin.ignore(2); return 0;
}