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.util.stream.IntStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.function.Supplier;
import java.util.ArrayList;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.util.stream.Collectors;
import java.util.List;
import java.util.stream.Stream;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author out_of_the_box
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(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 {
        List<List<Integer>> index;
        int[][] a;
        MiscUtility ut = new MiscUtility(false);

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            a = new int[2][n];
            for (int i = 0; i < n; i++) {
                a[0][i] = in.nextInt();
                a[0][i]--;
            }
            for (int i = 0; i < n; i++) {
                a[1][i] = in.nextInt();
                a[1][i]--;
            }
            Map<Integer, Integer> counts = new HashMap<>();
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < 2; j++) {
                    add(counts, a[j][i]);
                }
            }
            ut.printDebug(Suppliers.of(Arrays.stream(a[0]).boxed().collect(Collectors.toList())), "a[0]",
                    Suppliers.of(Arrays.stream(a[1]).boxed().collect(Collectors.toList())), "a[1]");
            ut.printDebug(counts, "counts");
            for (int i = 0; i < n; i++) {
                if (counts.getOrDefault(i, 0) != 2) {
                    out.println(-1);
                    return;
                }
            }
            index = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                index.add(new ArrayList<>());
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < 2; j++) {
                    int val = a[j][i];
                    index.get(val).add(i);
                }
            }
            ut.printDebug(index, "index");
            int ans = 0;
            boolean[] dis = new boolean[n];
//        int[] p = new int[n];
            boolean[] dans = new boolean[n];
            int[] cy = new int[n];
            int cz = 0;
            boolean[] tb = new boolean[n];
            for (int i = 0; i < n; i++) {
                ut.printDebug(i, "i");
                if (dis[i]) continue;
                if (a[0][i] == a[1][i]) continue;
                dis[i] = true;
                int curr = i;
                boolean cb = true;
                int tans = 1;
                cz = 0;
                cy[cz] = i;
                tb[cz] = true;
                cz++;
                int tc = 0;
                while (true) {
                    ut.printDebug(curr, "curr");
                    int nx = getOther(curr, tc);
                    boolean nb;
                    if (a[tc][nx] == a[tc][curr]) {
                        nb = !cb;
                        tc = (tc + 1) % 2;
                    } else {
                        nb = cb;
                    }
//                boolean nb = (a[0][nx] == a[0][curr]) == (!cb);
                    if (nx == i) {
                        if (!nb) {
                            out.println(-1);
                            return;
                        }
                        break;
                    } else {
                        dis[nx] = true;
                        curr = nx;
                        cb = nb;
                        cy[cz] = nx;
                        tb[cz] = nb;
                        cz++;
                        if (nb) tans++;
                    }
                }
                int ot = cz - tans;
                ut.printDebug(tans, "tans", ot, "ot");
                if (tans < ot) {
                    for (int j = 0; j < cz; j++) {
                        dans[cy[j]] = tb[j];
                    }
                    ans += tans;
                } else {
                    for (int j = 0; j < cz; j++) {
                        dans[cy[j]] = !tb[j];
                    }
                    ans += ot;
                }
            }
            out.println(ans);
            for (int i = 0; i < n; i++) {
                if (dans[i]) {
                    out.print((i + 1) + " ");
                }
            }
            out.println();
        }

        private int getOther(int i, int tc) {
//        int f = a[0][i];
            int f = a[tc][i];
            List<Integer> ind = index.get(f);
            for (int j = 0; j < 2; j++) {
                int in = ind.get(j);
                if (in != i) return in;
            }
            throw new IllegalStateException();
        }

        private void add(Map<Integer, Integer> mp, int key) {
            int val = mp.getOrDefault(key, 0);
            mp.put(key, val + 1);
        }

    }

    static class MiscUtility {
        public boolean debug;

        public MiscUtility() {
            debug = System.getProperty("ONLINE_JUDGE") == null;
        }

        public MiscUtility(boolean debug) {
            this.debug = debug;
        }

        public void printDebug(Object... objects) {
            if (debug) {
                boolean isName = false;
                Object prev = null;
                for (Object object : objects) {
                    if (isName) {
                        System.out.print(String.format("[%s: %s] ", object, prev.toString()));
                    } else {
                        prev = (object instanceof Supplier) ? (((Supplier) object).get()) : object;
                    }
                    isName = !isName;
                }
                System.out.println();
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println() {
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

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

        public InputReader(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 nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return nextString();
        }

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

        }

    }

    static class Suppliers {
        public static <T> Supplier<T> of(T object) {
            return () -> object;
        }

    }
}

