Once upon a time there was only one router in the well-known company Bmail. Years went by and over time new routers were purchased. Every time they bought a new router, they connected it to one of the routers bought before it. You are given the values p_i — the index of the router to which the i-th router was connected after being purchased (p_i < i).

There are n routers in Boogle in total now. Print the sequence of routers on the path from the first to the n-th router.

Input

The first line contains integer number n (2 ≤ n ≤ 200000) — the number of the routers. The following line contains n-1 integers p_2, p_3, ..., p_n (1 ≤ p_i < i), where p_i is equal to index of the router to which the i-th was connected after purchase.

Output

Print the path from the 1-st to the n-th router. It starts with 1 and ends with n. All the elements in the path should be distinct.

Examples

Input

8
1 1 2 2 3 2 5


Output

1 2 5 8 

Input

6
1 2 3 4 5


Output

1 2 3 4 5 6 

Input

7
1 1 2 3 4 3


Output

1 3 7 
import java.io.*;
import java.util.*;

public class Main {

    static int N;
    static int[] P;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        P = sc.nextIntArray(N-1, -1);

        writeSingleLine(solve());
    }

    static List<Integer> solve() {
        int[][] G = adjTree(N, P);
        Node[] nodes = orderFromLeaf(N, G, 0);
        Map<Integer, Node> map = new HashMap<>();
        for (Node node : nodes) {
            map.put(node.a, node);
        }

        List<Integer> path = new ArrayList<>();
        int cur = N-1;
        while(true) {
            path.add(cur+1);
            if( cur == 0 ) break;

            Node n = map.get(cur);
            cur = n.parent;
        }
        Collections.reverse(path);
        return path;
    }

    static class Node {
        int parent, a;

        public Node(int parent, int a) {
            this.parent = parent;
            this.a = a;
        }
    }

    static Node[] orderFromLeaf(int N, int[][] G, int root) {
        ArrayDeque<Node> q = new ArrayDeque<>();
        Node[] ret = new Node[N];
        int idx = N-1;
        q.add(new Node(-1, root));
        while(!q.isEmpty()) {
            Node n = q.poll();
            ret[idx--] = n;
            for (int next : G[n.a]) {
                if( next == n.parent ) continue;

                q.add(new Node(n.a, next));
            }
        }
        return ret;
    }

    static int[][] adjTree(int N, int[] paths) {
        int[] A = new int[paths.length];
        int[] B = new int[paths.length];

        for (int i = 0; i < paths.length; i++) {
            A[i] = paths[i];
            B[i] = i+1;
        }
        return adjB(N, A, B);
    }

    static int[][] adjB(int n, int[] from, int[] to) {
        int[][] adj = new int[n][];
        int[] cnt = new int[n];
        for (int f : from) {
            cnt[f]++;
        }
        for (int t : to) {
            cnt[t]++;
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new int[cnt[i]];
        }
        for (int i = 0; i < from.length; i++) {
            adj[from[i]][--cnt[from[i]]] = to[i];
            adj[to[i]][--cnt[to[i]]] = from[i];
        }
        return adj;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

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

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(List<Integer> as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.size(); i++) {
            if( i != 0 ) pw.print(" ");
            pw.print(as.get(i));
        }
        pw.println(); pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg == null ? "null" : arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        for (int i = 0; i < array.length; i++) {
            if( i != 0 ) System.out.print(" ");
            System.out.print(array[i]);
        }
        System.out.println();
    }

    static int lowerBound(int[] array, int value) {
        int low = 0, high = array.length, mid;
        while( low < high ) {
            mid = ((high - low) >>> 1) + low;
            if( array[mid] < value ) low = mid + 1;
            else high = mid;
        }
        return low;
    }

    static int upperBound(int[] array, int value) {
        int low = 0, high = array.length, mid;
        while( low < high ) {
            mid = ((high - low) >>> 1) + low;
            if( array[mid] <= value ) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}
