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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author KharYusuf
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "KharYusuf", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastReader in = new FastReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            GColumnsSwaps solver = new GColumnsSwaps();
            int testCount = Integer.parseInt(in.next());
            for (int i = 1; i <= testCount; i++)
                solver.solve(i, in, out);
            out.close();
        }
    }

    static class GColumnsSwaps {
        ArrayList<pair<Integer, Integer>>[] a;
        boolean[] vis;
        ArrayList<Integer> component;
        int[] color;
        int z;

        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt();
            int[][] arr = new int[2][n];
            a = new ArrayList[n];
            for (int i = 0; i < 2; i++) for (int j = 0; j < n; j++) arr[i][j] = s.nextInt() - 1;
            for (int i = 0; i < n; i++) a[i] = new ArrayList<>();
            int[][] r = new int[2][n], c = new int[2][n];
            for (int i = 0; i < 2; i++) Arrays.fill(r[i], -1);
            int[] ptr = new int[n], f = new int[n];
            for (int i = 0; i < n; i++) {
                f[arr[0][i]]++;
                f[arr[1][i]]++;
                if (f[arr[0][i]] > 2 || f[arr[1][i]] > 2) {
                    w.println(-1);
                    return;
                }
                if (arr[0][i] == arr[1][i]) continue;
                c[ptr[arr[0][i]]][arr[0][i]] = i;
                c[ptr[arr[1][i]]][arr[1][i]] = i;
                r[ptr[arr[0][i]]++][arr[0][i]] = 0;
                r[ptr[arr[1][i]]++][arr[1][i]] = 1;
            }
            for (int i = 0; i < n; i++) {
                //if (n == 3) w.println(r[0][i] + " " + r[1][i] + " " + c[0][i] + " " + c[1][i]);
                if (r[0][i] == -1) continue;
                a[c[0][i]].add(new pair<>(c[1][i], r[0][i] == r[1][i] ? 1 : 0));
                a[c[1][i]].add(new pair<>(c[0][i], r[0][i] == r[1][i] ? 1 : 0));
            }
            color = new int[n];
            vis = new boolean[n];
            ArrayList<Integer> ans = new ArrayList<>();
            for (int i = 0; i < n; i++)
                if (!vis[i]) {
                    component = new ArrayList<>();
                    z = 0;
                    if (!dfs(i)) {
                        w.println(-1);
                        return;
                    }
                    if (z < component.size() - z) {
                        for (int j : component) if (color[j] == 0) ans.add(j + 1);
                    } else for (int j : component) if (color[j] == 1) ans.add(j + 1);
                }
            w.println(ans.size());
            for (int i : ans) w.print(i + " ");
            w.println();
        }

        boolean dfs(int cur) {
            vis[cur] = true;
            component.add(cur);
            if (color[cur] == 0) z++;
            for (pair<Integer, Integer> i : a[cur]) {
                if (vis[i.x]) {
                    if ((color[i.x] ^ i.y) != color[cur]) return false;
                    continue;
                }
                color[i.x] = color[cur] ^ i.y;
                if (!dfs(i.x)) return false;
            }
            return true;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {

            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {

                curChar = 0;

                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }

            return buf[curChar++];
        }

        public int nextInt() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public String next() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            StringBuilder res = new StringBuilder();

            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<pair<U, V>> {
        public U x;
        public V y;

        public pair(U x, V y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair<U, V> other) {
            int i = x.compareTo(other.x);
            if (i != 0) return i;
            return y.compareTo(other.y);
        }

        public String toString() {
            return x.toString() + " " + y.toString();
        }

        public boolean equals(Object obj) {
            if (this.getClass() != obj.getClass()) return false;
            pair<U, V> other = (pair<U, V>) obj;
            return x.equals(other.x) && y.equals(other.y);
        }

        public int hashCode() {
            return 31 * x.hashCode() + y.hashCode();
        }

    }
}

