You are given a table a of size 2 × n (i.e. two rows and n columns) consisting of integers from 1 to n.

In one move, you can choose some column j (1 ≤ j ≤ n) and swap values a_{1, j} and a_{2, j} in it. Each column can be chosen no more than once.

Your task is to find the minimum number of moves required to obtain permutations of size n in both first and second rows of the table or determine if it is impossible to do that.

You have to answer t independent test cases.

Recall that the permutation of size n is such an array of size n that contains each integer from 1 to n exactly once (the order of elements doesn't matter).

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of columns in the table. The second line of the test case contains n integers a_{1, 1}, a_{1, 2}, ..., a_{1, n} (1 ≤ a_{1, i} ≤ n), where a_{1, i} is the i-th element of the first row of the table. The third line of the test case contains n integers a_{2, 1}, a_{2, 2}, ..., a_{2, n} (1 ≤ a_{2, i} ≤ n), where a_{2, i} is the i-th element of the second row of the table.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case print the answer: -1 if it is impossible to obtain permutation of size n in both first and the second rows of the table, or one integer k in the first line, where k is the minimum number of moves required to obtain permutations in both rows, and k distinct integers pos_1, pos_2, ..., pos_k in the second line (1 ≤ pos_i ≤ n) in any order — indices of columns in which you need to swap values to obtain permutations in both rows. If there are several answers, you can print any.

Example

Input


6
4
1 2 3 4
2 3 1 4
5
5 3 5 1 4
1 2 3 2 4
3
1 2 1
3 3 2
4
1 2 2 1
3 4 3 4
4
4 3 1 4
3 2 2 1
3
1 1 2
3 2 2


Output


0

2
2 3 
1
1 
2
3 4 
2
3 4 
-1
import java.lang.*;
import java.util.*;

public class Main {
    static class Pair {
        int x, y;
        Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    public static int cnt0, cnt1;
    public static int[] color, comp;
    public static Vector<Vector<Pair>> g;
    public static Vector<Vector<Integer>> poz;

    public static void DFS(int node, int c, int cmp, int[] color, int[] comp) {
        color[node] = c;
        if (color[node] == 0)
            ++cnt0;
        else
            ++cnt1;
        comp[node] = cmp;
        for (Pair p : g.get(node)) {
            int vecin = p.x, change = p.y;
            if (color[vecin] == -1)
                DFS(vecin, c ^ change, cmp, color, comp);
        }
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            boolean bad = false;
            int[][] a = new int[2][n];
            color = new int[n];
            comp = new int[n];
            Arrays.fill(color, -1);
            Arrays.fill(comp, -1);
            g = new Vector<>();
            poz = new Vector<>();
            for (int i = 0; i < n; ++i) {
                poz.add(i, new Vector<>(0));
                g.add(i, new Vector<>(0));
            }

            for (int i = 0; i < 2; ++i) {
                for (int j = 0; j < n; ++j) {
                    a[i][j] = in.nextInt() - 1;
                    poz.get(a[i][j]).add(j);
                }
            }

            for (int i = 0; i < n; ++i) {
                if (poz.get(i).size() != 2) {
                    bad = true;
                    break;
                }
                int c1 = poz.get(i).get(0), c2 = poz.get(i).get(1);
                if (c1 == c2)
                    continue;
                int r1 = (a[0][c1] != i ? 1 : 0), r2 = (a[0][c2] != i ? 1 : 0);
                g.get(c1).add(new Pair(c2, (r1 == r2 ? 1 : 0)));
                g.get(c2).add(new Pair(c1, (r1 == r2 ? 1 : 0)));
            }

            Vector<Pair> colcnt = new Vector<>(0);
            int cnt = 0, ans = 0;
            for (int i = 0; i < n; ++i) {
                if (color[i] == -1) {
                    cnt0 = cnt1 = 0;
                    DFS(i, 0, cnt, color, comp);
                    ++cnt;
                    colcnt.add(new Pair(cnt0, cnt1));
                    ans += Math.min(cnt0, cnt1);
                }
            }

            for (int i = 0; i < n; ++i) {
                for (Pair p : g.get(i)) {
                    if ((color[i] ^ color[p.x]) != p.y) {
                        bad = true;
                        break;
                    }
                }
            }

            if (bad) {
                System.out.println(-1);
                continue;
            }

            System.out.println(ans);
            for (int i = 0; i < n; ++i) {
                int change = (colcnt.get(comp[i]).x < colcnt.get(comp[i]).y ? 1 : 0);
                if ((color[i] ^ change) == 1)
                    System.out.print((i + 1) + " ");
            }
            System.out.println();
        }
    }
}
