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;
vector<int> path;
void dfs(vector<int> adj[], int start, int n) {
  if (!adj[start].size()) {
    path.push_back(start);
    if (start == n) {
      for (int i = 0; i < path.size(); i++) {
        cout << path[i] + 1 << " ";
      }
      cout << endl;
    }
    path.pop_back();
  }
  for (auto u : adj[start]) {
    path.push_back(start);
    dfs(adj, u, n);
    path.pop_back();
  }
}
int main() {
  int n;
  cin >> n;
  vector<int> adj[n];
  for (int i = 1; i < n; i++) {
    int x;
    cin >> x;
    adj[x - 1].push_back(i);
  }
  dfs(adj, 0, n - 1);
}
