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 
#include <bits/stdc++.h>
using namespace std;
void insert(vector<int> adj[], int u, int v) { adj[u].push_back(v); }
vector<int> a;
bool find(vector<int> adj[], int x, int n) {
  a.push_back(x);
  if (x == n) {
    return true;
  }
  for (int d : adj[x]) {
    if (find(adj, d, n)) {
      return true;
    }
  }
  a.pop_back();
  return false;
}
void print(vector<int> adj[], int n) {
  for (int i = 1; i < n + 1; i++) {
    cout << i << "=>";
    for (int x : adj[i]) {
      cout << x << " ";
    }
    cout << endl;
  }
}
int main() {
  int n;
  cin >> n;
  vector<int> v(n + 1, -1);
  for (int i = 2; i < n + 1; i++) {
    cin >> v[i];
  }
  vector<int> adj[n + 1];
  for (int i = 2; i < n + 1; i++) {
    insert(adj, v[i], i);
  }
  find(adj, 1, n);
  for (int i = 0; i < a.size(); i++) {
    cout << a[i] << " ";
  }
  return 0;
}
