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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;

public class Task7 {
    boolean[] visited;
    int[][] ar;
    int[][] orgAr;
    int[][] colsOfANum;

    public static void main(String[] args) throws IOException  {
        new Task7().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int t = Integer.parseInt(f.readLine());
        for (int t1 = 0; t1 < t; t1++) {
            int n = Integer.parseInt(f.readLine());
            int[][] count = new int[n + 1][2];
            ar = new int[2][n];
            colsOfANum = new int[n + 1][2];
            orgAr = new int[2][n];
            for (int j = 0; j < 2; j++) {
                StringTokenizer tokenizer = new StringTokenizer(f.readLine());
                for (int i = 0; i < n; i++) {
                    ar[j][i] = Integer.parseInt(tokenizer.nextToken());
                    orgAr[j][i] = ar[j][i];
                    if (colsOfANum[ar[j][i]][0] == 0) {
                        colsOfANum[ar[j][i]][0] = i;
                    } else {
                        colsOfANum[ar[j][i]][1] = i;
                    }
                    count[ar[j][i]][j]++;
                }
            }

            boolean impossible = false;
            for (int i = 1; i <= n; i++) {
                if (count[i][0] + count[i][1] != 2) {
                    impossible = true;
                    break;
                }
            }
            if (impossible) {
                out.println(-1);
                continue;
            }

            visited = new boolean[n];
            ArrayList<Integer> swaps = new ArrayList<Integer>();
            for (int i = 0; i < n; i++) {
                if (!visited[i]) {
                    if (ar[0][i] == ar[1][i]) continue;
                    int num = ar[0][i];
                    ArrayList<Integer> swaps1 = new ArrayList<Integer>();
                    ArrayList<Integer> swaps2 = new ArrayList<Integer>();
                    trySwap(i, true, num, swaps1, swaps2);

                    //System.out.println(possible1 + " " + possible2 + " " + swaps1.size() + " " + swaps2.size());
                    if (swaps1.size() < swaps2.size()) {
                        swaps.addAll(swaps1);
                    } else {
                        swaps.addAll(swaps2);
                    }
                }
            }

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



            out.println(swaps.size());
            if (!swaps.isEmpty()) {
                out.print(swaps.get(0) + 1);
                for (int i = 1; i < swaps.size(); i++) {
                    out.print(" ");
                    out.print(swaps.get(i) + 1);
                }
            }
            out.println();
        }

        out.close();
    }

    private void cleanState(int col) {
        //System.out.println(col);
        if (visited[col]) {
            ar[0][col] = orgAr[0][col];
            ar[1][col] = orgAr[1][col];
            visited[col] = false;
            for (int i = 0; i < 2; i++) {
                if (colsOfANum[ar[i][col]][0] != col) {
                    if (visited[colsOfANum[ar[i][col]][0]]) {
                        cleanState(colsOfANum[ar[i][col]][0]);
                    }
                } else {
                    if (visited[colsOfANum[ar[i][col]][0]]) {
                        cleanState(colsOfANum[ar[i][col]][1]);
                    }
                }
            }
        }
    }

    private boolean trySwap(int col, boolean isUp, int num, ArrayList<Integer> swaps1, ArrayList<Integer> swaps2) {
        int indexLooking;
        int indexOther;
        if (isUp) {
            indexLooking = 0;
            indexOther = 1;
        } else {
            indexLooking = 1;
            indexOther = 0;
        }
        //System.out.println(col + " " + isUp + " " + num + " " + (ar[indexLooking][col] != num));

        if (visited[col]) {
            if (ar[indexLooking][col] != num) return false;
            else return true;
        }


        if (ar[indexLooking][col] != num) {
            swaps1.add(col);
            int temp = ar[indexOther][col];
            ar[indexOther][col] = ar[indexLooking][col];
            ar[indexLooking][col] = temp;
        } else swaps2.add(col);

        visited[col] = true;
        boolean possible = true;
        if (colsOfANum[ar[indexLooking][col]][0] != col) {
            possible = possible && trySwap(colsOfANum[ar[indexLooking][col]][0], !isUp, ar[indexLooking][col], swaps1, swaps2);
        } else {
            possible = possible && trySwap(colsOfANum[ar[indexLooking][col]][1], !isUp, ar[indexLooking][col], swaps1, swaps2);
        }
        if (colsOfANum[ar[indexOther][col]][0] != col) {
            possible = possible && trySwap(colsOfANum[ar[indexOther][col]][0], isUp, ar[indexOther][col], swaps1, swaps2);
        } else {
            possible = possible && trySwap(colsOfANum[ar[indexOther][col]][1], isUp, ar[indexOther][col], swaps1, swaps2);
        }

        return possible;
    }
}
