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 <algorithm>
#include <iostream>

using namespace std;
const int maxn = 2e5 + 5;
int a[maxn], b[maxn];
int main(void)
{
    int n;
    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, last = -1;
    for (int i = 0; i < n; ++i)
    {
        if(last!=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" << endl;
                return 0;
            }
        }
        last = a[i];
    }
    cout << "Yes" << endl;
    for (int i = 0; i < n; ++i)
        cout << b[i] << " ";
    cout << endl;

    return 0;
}