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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.util.Random;
import java.util.StringTokenizer;

public class Main {

    final long b = 31;
    String fileName = "";


    //////////////////////    SOLUTION   SOLUTION  SOLUTION    //////////////////////////////
    int INF = 1000_000_000 +100;
    long MODULO = 1000_000_000 + 7;
    int MAX_VALUE = 1000_1000;
    int[][] steps = {{0, 1}, {1, 0}, {-1, 0}, {0, -1}};
    private final static Random rnd = new Random();
    double eps = 1e-7;
    class Dsu{
        int[] parent;
        int countSets;
        Dsu(int n){
            parent = new int[n];
            countSets = n;
            for (int i=0; i<n; ++i){
                parent[i] = i;
            }
        }
        int findSet(int a){
            if (a == parent[a]) return a;
            parent[a] = findSet(parent[a]);
            return parent[a];
        }
        void unionSets(int a, int b){
            a = findSet(a);
            b = findSet(b);
            if (a != b){
                parent[a] = b;
                countSets--;
            }
        }
    }
    class Sector implements Comparable<Sector>{
        int ind, val;
        Sector(int ind, int val){
            this.ind = ind;
            this.val = val;
        }

        @Override
        public int compareTo(Sector o) {
            return Integer.compare(this.val, o.val);
        }
    }
    void solve() throws IOException {
        int n = readInt();
        int[] arr = new int[n];
        int[] ans = new int[n];

        for (int i=0; i<n; ++i) arr[i] = readInt() - 1;
        boolean[] used = new boolean[n];
        ArrayList<Integer> curCycle = new ArrayList<>();
        ArrayList<Integer>[] evenCycle = new ArrayList[n+1];
        for (int i=0; i<=n; ++i) evenCycle[i] = new ArrayList<>();

        for (int i=0; i<n; ++i){
            curCycle.clear();
            if (used[i]) continue;
            int cur = i;
            while (!used[cur]){
                curCycle.add(cur);
                used[cur] = true;
                cur = arr[cur];
            }
            if (curCycle.size() % 2 == 1){
                int l = 0;
                int r = curCycle.size() / 2 + 1;
                for (int j=0; j<curCycle.size()/2; ++j){
                    ans[curCycle.get(l+j)] = curCycle.get(r+j);
                    ans[curCycle.get(r+j)] = curCycle.get(l+j+1);
                }
                ans[curCycle.get(curCycle.size()/2)] = curCycle.get(0);
                continue;
            }
            if (evenCycle[curCycle.size()].size() == 0){
                evenCycle[curCycle.size()].addAll(curCycle);
                continue;
            }
            for (int j=0; j<curCycle.size() - 1; ++j){
                ans[curCycle.get(j)] = evenCycle[curCycle.size()].get(j);
                ans[evenCycle[curCycle.size()].get(j)] = curCycle.get(j+1);
            }
            ans[curCycle.get(curCycle.size() - 1)] = evenCycle[curCycle.size()].get(curCycle.size() - 1);
            ans[evenCycle[curCycle.size()].get(curCycle.size() - 1)] = curCycle.get(0);
            evenCycle[curCycle.size()].clear();
            continue;
        }
        for (int i=0; i<=n; ++i){
            if (evenCycle[i].size() > 0) {
                out.println(-1);
                return;
            }
        }
        for (int i: ans) out.print(i+1+" ");
    }

    boolean isPrime(int n){
        for (int i=2; i*i<=n; ++i){
            if (n%i==0) return false;
        }
        return true;
    }
    class Edge implements Comparable<Edge>{
        int from, to, num, dist;
        Edge(int from, int to, int dist, int num){
            this.from = from;
            this.to = to;
            this.num = num;
            this.dist = dist;
        }

        @Override
        public int compareTo(Edge o) {
            return Integer.compare(this.dist, o.dist);
        }
    }
    class Number implements Comparable<Number>{
        int x, cost;
        Number(int x, int cost){
            this.x = x;
            this.cost = cost;
        }

        @Override
        public int compareTo(Number o) {
            return Integer.compare(this.cost, o.cost);
        }
    }

    void readUndirectedGraph (int n, int m, int[][] graph) throws IOException{
        Edge[] edges = new Edge[m];
        int[] countEdges = new int[n];
        for (int i=0; i<m; ++i){
            int from = readInt() - 1;
            int to = readInt() - 1;
            countEdges[from]++;
            countEdges[to]++;
            edges[i] = new Edge(from, to, 0, 0);
        }
        for (int i=0; i<n; ++i) {
            graph[i] = new int[countEdges[i]];
        }
        for (int i=0; i<m; ++i){
            graph[edges[i].from][--countEdges[edges[i].from]] = edges[i].to;
            graph[edges[i].to][-- countEdges[edges[i].to]] = edges[i].from;
        }
    }
    class Vertex implements Comparable<Vertex>{
        int i, j, plus;
        Vertex(int i, int j, int plus){
            this.i = i;
            this.j = j;
            this.plus = plus;
        }

        @Override
        public int compareTo(Vertex o) {
            return Integer.compare(this.plus, o.plus);
        }
    }



    ///////////////////////////////////////////////////////////////////////////////////////////



    class SparseTable{
        int[][] rmq;
        int[] logTable;
        int n;
        SparseTable(int[] a){
            n = a.length;
            logTable = new int[n+1];
            for(int i = 2; i <= n; ++i){
                logTable[i] = logTable[i >> 1] + 1;
            }
            rmq = new int[logTable[n] + 1][n];
            for(int i=0; i<n; ++i){
                rmq[0][i] = a[i];
            }

            for(int k=1; (1 << k) < n; ++k){
                for(int i=0; i + (1 << k) <= n; ++i){
                    int max1 = rmq[k - 1][i];
                    int max2 = rmq[k-1][i + (1 << (k-1))];
                    rmq[k][i] = Math.max(max1, max2);
                }
            }
        }

        int max(int l, int r){
            int k = logTable[r - l];
            int max1 = rmq[k][l];
            int max2 = rmq[k][r - (1 << k) + 1];
            return Math.max(max1, max2);
        }
    }
    long checkBit(long mask, int bit){
        return (mask >> bit) & 1;
    }

    static int checkBit(int mask, int bit) {
        return (mask >> bit) & 1;
    }
    boolean isLower(char c){
        return c >= 'a' && c <= 'z';
    }

    ////////////////////////////////////////////////////////////

    class SegmentTree{
        int[] t;
        int n;
        SegmentTree(int n){
            t = new int[4*n];
            build(new int[n+1], 1, 1, n);
        }
        void build (int a[], int v, int tl, int tr) {
            if (tl == tr)
                t[v] = a[tl];
            else {
                int tm = (tl + tr) / 2;
                build (a, v*2, tl, tm);
                build (a, v*2+1, tm+1, tr);
            }
        }

        void update (int v, int tl, int tr, int l, int r, int add) {
            if (l > r)
                return;
            if (l == tl && tr == r)
                t[v] += add;
            else {
                int tm = (tl + tr) / 2;
                update (v*2, tl, tm, l, Math.min(r,tm), add);
                update (v*2+1, tm+1, tr, Math.max(l,tm+1), r, add);
            }
        }

        int get (int v, int tl, int tr, int pos) {
            if (tl == tr)
                return t[v];
            int tm = (tl + tr) / 2;
            if (pos <= tm)
                return t[v] + get (v*2, tl, tm, pos);
            else
                return t[v] + get (v*2+1, tm+1, tr, pos);
        }
    }
    class Fenwik {
        long[] t;
        int length;

        Fenwik(int[] a) {
            length = a.length + 100;
            t = new long[length];

            for (int i = 0; i < a.length; ++i) {
                inc(i, a[i]);
            }
        }

        void inc(int ind, int delta) {
            for (; ind < length; ind = ind | (ind + 1)) {
                t[ind] = Math.max(delta, t[ind]);
            }
        }

        long getMax(int r) {
            long sum = 0;
            for (; r >= 0; r = (r & (r + 1)) - 1) {
                sum = Math.max(sum, t[r]);
            }
            return sum;
        }
    }
    int gcd(int a, int b){
        return b == 0 ? a : gcd(b, a%b);
    }
    long gcd(long a, long b){
        return b == 0 ? a : gcd(b, a%b);
    }
    double binPow(double a, int pow){
        if (pow == 0) return 1;
        if (pow % 2 == 1) {
            return a * binPow(a, pow - 1);
        } else {
            double c = binPow(a, pow / 2);
            return c * c;
        }
    }
    long binPow(long a, long b, long m) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 1) {
            return ((a % m) * (binPow(a, b - 1, m) % m)) % m;
        } else {
            long c = binPow(a, b / 2, m);
            return (c * c) % m;
        }

    }
    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) min = Math.min(min, value);
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) max = Math.max(max, value);
        return max;
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        new Main().run();
    }

    void run() throws NumberFormatException, IOException {
        solve();
        out.close();
    };

    BufferedReader in;
    PrintWriter out;

    StringTokenizer tok;
    String delim = " ";

    Main() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }

        }
        tok = new StringTokenizer("");
    }

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) {
                return null;
            }

            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken();
    }

    int readInt() throws NumberFormatException, IOException {
        return Integer.parseInt(readString());
    }
    byte readByte() throws NumberFormatException, IOException {
        return Byte.parseByte(readString());
    }
    int[] readIntArray (int n) throws NumberFormatException, IOException {
        int[] a = new int[n];
        for(int i=0; i<n; ++i){
            a[i] = readInt();
        }
        return a;
    }

    Integer[] readIntegerArray (int n) throws NumberFormatException, IOException {
        Integer[] a = new Integer[n];
        for(int i=0; i<n; ++i){
            a[i] = readInt();
        }
        return a;
    }

    long readLong() throws NumberFormatException, IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(readString());
    }
}
