A permutation of length n is an array containing each integer from 1 to n exactly once. For example, q = [4, 5, 1, 2, 3] is a permutation. For the permutation q the square of permutation is the permutation p that p[i] = q[q[i]] for each i = 1... n. For example, the square of q = [4, 5, 1, 2, 3] is p = q2 = [2, 3, 4, 5, 1].

This problem is about the inverse operation: given the permutation p you task is to find such permutation q that q2 = p. If there are several such q find any of them.

Input

The first line contains integer n (1 ≤ n ≤ 106) — the number of elements in permutation p.

The second line contains n distinct integers p1, p2, ..., pn (1 ≤ pi ≤ n) — the elements of permutation p.

Output

If there is no permutation q such that q2 = p print the number "-1".

If the answer exists print it. The only line should contain n different integers qi (1 ≤ qi ≤ n) — the elements of the permutation q. If there are several solutions print any of them.

Examples

Input

4
2 1 4 3


Output

3 4 2 1


Input

4
2 1 3 4


Output

-1


Input

5
2 3 4 5 1


Output

4 5 1 2 3
import java.io.*;
import java.util.*;

public class Main {

    private static final long MOD = 998244353;

    static int[] readArray(int size, InputReader in, boolean subOne) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextInt() + (subOne ? -1 : 0);
        }
        return a;
    }

    static long[] readLongArray(int size, InputReader in) {
        long[] a = new long[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextLong();
        }
        return a;
    }

    static void sortArray(int[] a) {
        Random random = new Random();

        for (int i = 0; i < a.length; i++) {
            int randomPos = random.nextInt(a.length);
            int t = a[i];
            a[i] = a[randomPos];
            a[randomPos] = t;
        }
        Arrays.sort(a);
    }


    public static void main(String[] args) throws FileNotFoundException {
//        InputReader in = new InputReader(new FileInputStream("input.txt"));
//        PrintWriter out = new PrintWriter(new BufferedOutputStream(new FileOutputStream("milkvisits.out")));
//
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int n = in.nextInt();
        int[] p = readArray(n, in, true);
        boolean[] visited = new boolean[n];
        Map<Integer, List<List<Integer>>> evenCycles = new HashMap<>();
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            if (!visited[i]) {
                List<Integer> cycle = new ArrayList<>();
                cycle.add(i);
                int k = i;
                visited[k] = true;
                while (p[k] != i) {
                    cycle.add(p[k]);
                    k = p[k];
                    visited[k] = true;
                }
                int size = cycle.size();
                if (size % 2 == 0) {
                    if (!evenCycles.containsKey(size)) {
                        evenCycles.put(size, new ArrayList<>());
                    }
                    evenCycles.get(size).add(cycle);
                } else {
                    int odd = size / 2 + 1;
                    int even = 0;
                    for (int j = 0; j < size; j++) {
                        if (j % 2 == 0) {
                            ans[cycle.get(even % size)] = cycle.get(odd % size);
                            even++;
                        } else {
                            ans[cycle.get(odd % size)] = cycle.get(even % size);
                            odd++;
                        }
                    }
                }
            }
        }

        for (int size : evenCycles.keySet()) {
            List<List<Integer>> cycles = evenCycles.get(size);
            if (cycles.size() % 2 != 0) {
                out.println(-1);
                out.close();
                return;
            }
            for (int i = 0; i < cycles.size(); i += 2) {
                List<Integer> cycle1 = cycles.get(i);
                List<Integer> cycle2 = cycles.get(i + 1);
                int even = 0;
                int odd = 0;
                for (int j = 0; j < size * 2; j++) {
                    if (j % 2 == 0) {
                        ans[cycle1.get(even % size)] = cycle2.get(odd % size);
                        even++;
                    } else {
                        ans[cycle2.get(odd % size)] = cycle1.get(even % size);
                        odd++;
                    }
                }
            }
        }
        outputArray(ans, out, true);

        out.close();
    }

    private static void outputArray(int[] ans, PrintWriter out, boolean addOne) {
        StringBuilder str = new StringBuilder();
        for (int i = 0; i < ans.length; i++) {
            long an = ans[i] + (addOne ? 1 : 0);
            str.append(an).append(' ');
        }
        out.println(str);
    }

    private static void outputArray(List<Integer> ans, PrintWriter out, boolean addOne) {
        StringBuilder str = new StringBuilder();
        for (int j = 0; j < ans.size(); j++) {
            long i = ans.get(j);
            long an = i + (addOne ? 1 : 0);
            str.append(an);
            if (j < ans.size() - 1) {
                str.append(' ');
            }
        }
        out.println(str);
//        out.flush();
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }

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

        private List<Integer>[] readTree(int n) {
            return readGraph(n, n - 1);
        }

        private List<Integer>[] readGraph(int n, int m) {
            List<Integer>[] result = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                result[i] = new ArrayList<>();
            }
            for (int i = 0; i < m; i++) {
                int u = nextInt() - 1;
                int v = nextInt() - 1;
                result[u].add(v);
                result[v].add(u);
            }
            return result;
        }

        private Map<Integer, Long>[] readWeightedGraph(int n, int m) {
            Map<Integer, Long>[] result = new HashMap[n];
            for (int i = 0; i < n; i++) {
                result[i] = new HashMap<>();
            }
            for (int i = 0; i < m; i++) {
                int u = nextInt() - 1;
                int v = nextInt() - 1;
                long w = nextLong();
                result[u].put(v, Math.min(w, result[u].getOrDefault(v, Long.MAX_VALUE)));
                result[v].put(u, Math.min(w, result[v].getOrDefault(u, Long.MAX_VALUE)));
            }
            return result;
        }

    }
}