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;
set<int> ans;
void DFS(int Node, vector<vector<int>>& graph, vector<bool>& visted) {
  ans.insert(Node);
  visted[Node] = 1;
  int length;
  for (auto child : graph[Node]) {
    if (!visted[child]) {
      if (child == 1) {
        cout << 1;
        for (auto i : ans) cout << " " << i;
        return;
      }
      DFS(child, graph, visted);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int num, number, Node = 2, t;
  cin >> num;
  t = num - 1;
  vector<vector<int>> graph(num + 1);
  while (t--) {
    cin >> number;
    graph[number].push_back(Node);
    graph[Node].push_back(number);
    Node++;
  }
  graph[num].push_back(number);
  vector<bool> visted(num + 1);
  DFS(num, graph, visted);
}
