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 + 1;

int n, a[N], b[N];

int main() {
    ios::sync_with_stdio(false); 
    cin.tie(NULL);

    cin >> n;
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) cin >> b[i];
    
    int j = 0, bef = -1;
    for (int i = 0; i < n; i++) {
        if (bef != a[i]) j = 0; 
        if (a[i] == b[i]) {
            for (; j < n; j++) {
                if (a[j] != a[i] && b[j] != a[i]) {
                    swap(b[i], b[j]);
                    break;
                }
            }
            if (a[i] == b[i]) {
                cout << "No";
                return 0;
            }
        }
        bef = a[i];
    }
    cout << "Yes\n";
    for (int i = 0; i < n; i++) {
        if (i) cout << ' ';
        cout << b[i];
    }
}