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;
long long power(long long x, long long y, long long m) {
  long long r = 1;
  for (; y; y >>= 1) {
    if (y & 1) r = r * x % m;
    x = x * x % m;
  }
  return r;
}
const long long N = 205, M = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  srand(time(NULL));
  ;
  long long n, m, x = 0, k, i, t, ans = 0, j, y = 0, z = 4, c = 0;
  cin >> n;
  long long a[n];
  vector<long long> v;
  for (long long i = 1; i < n; i++) cin >> a[i];
  i = n - 1;
  v.push_back(n);
  while (a[i] != 1) {
    v.push_back(a[i]);
    i = a[i] - 1;
  }
  v.push_back(1);
  for (i = v.size() - 1; i >= 0; i--) cout << v[i] << " ";
}
