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 test_case;
  test_case = 1;
  while (test_case--) {
    long long int n;
    cin >> n;
    vector<int> a;
    a.push_back(0);
    for (long long int i = 0; i < n - 1; i++) {
      long long int t;
      cin >> t;
      a.push_back(t);
    }
    long long int k = n - 1;
    stack<long long int> s;
    vector<long long int> v;
    s.push(n);
    while (k != 0) {
      s.push(a[k]);
      k = a[k] - 1;
    }
    while (!s.empty()) {
      cout << s.top() << " ";
      s.pop();
    }
  }
  return 0;
}
