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 temp;
  if (y == 0) return 1;
  temp = power(x, y / 2);
  if (y % 2 == 0)
    return temp * temp;
  else {
    if (y > 0)
      return x * temp * temp;
    else
      return (temp * temp) / x;
  }
}
long long fast_power(long long x, long long n, long mood) {
  if (n == 0)
    return 1;
  else if (n % 2 == 0)
    return fast_power(x * x, n / 2, mood);
  else
    return (x * fast_power((x * x) % mood, (n - 1) / 2, mood));
}
int arr[200010];
int n;
void solve(int c) {
  if (c == 0) return;
  solve(arr[c]);
  cout << c << " ";
}
int main() {
  while (cin >> n) {
    for (int i = 2; i <= n; i++) cin >> arr[i];
    solve(n);
    cout << "\n";
  }
  return 0;
}
