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;
vector<long long int> v;
set<long long int> s1;
set<long long int> s2;
set<string> st2;
vector<long long int> v1;
vector<long long int> v2;
vector<long long int> v3;
vector<long long int> v4;
vector<long long int> v5;
vector<pair<long long int, long long int> > v6;
vector<pair<long long int, long long int> > v16;
vector<string> v7;
vector<string> v8;
vector<char> v9;
vector<char> v99;
set<char> s11;
set<char> s22;
vector<double> v11;
list<long long int> l;
vector<vector<long long int> > b;
int main() {
  long long int n;
  cin >> n;
  long long int a[n];
  long long int b[n];
  b[1] = -1;
  for (long long int i = 2; i <= n; i++) {
    cin >> a[i];
    b[i] = a[i];
  }
  v.push_back(n);
  long long int x = n;
  while (1) {
    x = b[n];
    if (x == -1) break;
    v.push_back(x);
    n = x;
  }
  reverse(v.begin(), v.end());
  for (long long int i = 0; i < v.size(); i++) {
    cout << v[i] << " ";
  }
  cout << endl;
  return 0;
}
