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;
int main() {
  int temp, temp2;
  cin >> temp;
  vector<int> data;
  for (int i = 0; i < temp - 1; i++) {
    cin >> temp2;
    data.push_back(temp2);
  }
  int index = temp - 2;
  vector<int> final;
  final.push_back(temp);
  while (index >= 1) {
    int m = data[index];
    final.push_back(m);
    index = m - 2;
  }
  if (final[final.size() - 1] != 1) final.push_back(1);
  for (int i = final.size() - 1; i >= 0; i--) cout << final[i] << " ";
  cout << endl;
  return 0;
}
