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() {
  long long t;
  t = 1;
  while (t--) {
    int n;
    cin >> n;
    int a[n + 1];
    a[1] = 0;
    for (int i = 2; i <= n; i++) cin >> a[i];
    vector<int> v;
    v.push_back(n);
    n = a[n];
    v.push_back(n);
    while (n != 1) {
      v.push_back(a[n]);
      n = a[n];
    }
    reverse(v.begin(), v.end());
    for (auto x : v) cout << x << " ";
  }
  return 0;
}
