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;
const int MAXN = 2e5 + 1;
const int MOD = 1e9 + 7;
long long a[MAXN], b[MAXN];
bool used[MAXN];
vector<int> g[MAXN];
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  ;
  long long n, m, cnt = 0, ans = 0;
  bool y = 0;
  cin >> n;
  a[1] = 1;
  for (int i = 2; i <= n; i++) {
    cin >> a[i];
  }
  cnt = n;
  while (cnt != 1) {
    ans++;
    b[ans] = cnt;
    cnt = a[cnt];
  }
  reverse(b + 1, b + ans + 1);
  cout << 1 << " ";
  for (int i = 1; i <= ans; i++) {
    cout << b[i] << " ";
  }
  return 0;
}
