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.*;
import java.util.*;

public class CFB {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000L * 1000L * 1000L + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    void solve() throws IOException {
        int T = nextInt();
        for (int i = 0; i < T; i++) {
            helper();
        }
    }

    List<List<Edge>> graph;
    boolean[] vis;
    class Edge {
        int type;
        int from;
        int to;
        public Edge(int type, int from, int to) {
            this.type = type;
            this.from = from;
            this.to = to;
        }

        @Override
        public String toString() {
            return type + " " + from + " " + to;
        }
    }
    void helper() throws IOException {
        int n = nextInt();
        int[] first = nextIntArr(n);
        int[] second = nextIntArr(n);
        int[] hist = new int[n];
        for (int v : first) {
            hist[v - 1]++;
        }
        for (int v : second) {
            hist[v - 1]++;
        }
        for (int v : hist) {
            if (v != 2) {
                outln(-1);
                return;
            }
        }
        graph = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            graph.add(new ArrayList<>());
        }
        addEdge(first);
        addEdge(second);
        addEdge(first, second);

        vis = new boolean[n];
        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (!vis[i]) {
                Set<Integer> all = new HashSet<>();
                Set<Integer> zero = new HashSet<>();
                dfs(-1, i, all, zero, 0);

                if (zero.size() < all.size() - zero.size()) {
                    res.addAll(zero);
                } else {
                    for (int v : all) {
                        if (!zero.contains(v)) {
                            res.add(v);
                        }
                    }
                }
            }
        }
        outln(res.size());
        for (int v : res) {
            out((1 + v) + " ");
        }
        outln("");
    }

    void dfs(int par, int cur, Set<Integer> all, Set<Integer> zero, int target) {
        if (vis[cur]) {
            return;
        }
        vis[cur] = true;
        if (target == 0) {
            zero.add(cur);
        }
        all.add(cur);
        for (Edge edge : graph.get(cur)) {
            if (edge.to != par) {
                dfs(cur, edge.to, all, zero, edge.type == 1 ? 1 - target : target);
            }
        }
    }

    void addEdge(int[] first, int[] second) {
        Map<Integer, Integer> has = new HashMap<>();
        for (int i = 0; i < first.length; i++) {
            has.put(first[i], i);
        }
        for (int i = 0; i < second.length; i++) {
            if (has.containsKey(second[i])) {
                int from = i;
                int to = has.get(second[i]);
                graph.get(from).add(new Edge(0, from, to));
                graph.get(to).add(new Edge(0, to, from));
            }
        }
    }

    void addEdge(int[] arr) {
        List<List<Integer>> ls = new ArrayList<>();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            ls.add(new ArrayList<>());
        }

        for (int i = 0; i < arr.length; i++) {
            ls.get(arr[i] - 1).add(i);
        }

        for (List<Integer> single : ls) {
            if (single.size() >= 2) {
                for (int i = 0; i < single.size(); i++) {
                    for (int j = i + 1; j < single.size(); j++) {
                        int from = single.get(i);
                        int to = single.get(j);
                        graph.get(from).add(new Edge(1, from, to));
                        graph.get(to).add(new Edge(1, to, from));
                    }
                }
            }
        }
    }

    void shuffle(long[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            long tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        outln(String.format("%.9f%n", val));
    }
    public CFB() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFB();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}
