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;
struct node {
  int val;
  shared_ptr<node> prev;
  shared_ptr<node> next;
};
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  shared_ptr<node> origin(new node);
  origin->val = 1;
  origin->prev = nullptr;
  origin->next = nullptr;
  vector<shared_ptr<node> > node_addr;
  shared_ptr<node> initial(new node);
  node_addr.push_back(initial);
  node_addr.push_back(origin);
  for (int i = 2; i < n + 1; i++) {
    int a;
    cin >> a;
    shared_ptr<node> newnode(new node);
    newnode->prev = node_addr[a];
    newnode->val = i;
    node_addr.push_back(newnode);
  }
  vector<int> order;
  shared_ptr<node> finder = node_addr[node_addr.size() - 1];
  while (true) {
    order.push_back(finder->val);
    if (finder->prev != nullptr) {
      finder = finder->prev;
    } else {
      break;
    }
  }
  reverse(order.begin(), order.end());
  for (int i = 0; i < order.size(); i++) {
    cout << order[i] << " ";
  }
  return 0;
}
