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 + 10;
const int MOD = 1e9 + 7;
const long long inf = 2e18;
int n, m;
int a[maxn];
vector<int> v;
void solve() {
  cin >> n;
  for (int i = 1; i < n; i++) {
    cin >> a[i];
    --a[i];
  }
  v.push_back(n - 1);
  int x = n - 1;
  while (x != 0) {
    x = a[x];
    v.push_back(x);
  }
  reverse(v.begin(), v.end());
  for (int i = 0; i < v.size(); i++) {
    if (i) cout << " ";
    cout << v[i] + 1;
  }
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  int test = 1;
  while (test--) {
    solve();
    cout << '\n';
  }
  return 0;
}
