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<bool> visitados;
vector<vector<int>> graf;
vector<int> padres;
void dfs(int origen) {
  visitados[origen] = true;
  for (int i : graf[origen]) {
    if (visitados[i] == false) {
      padres[i] = origen;
      dfs(i);
    }
  }
}
int main() {
  int n;
  cin >> n;
  graf.resize(n + 1);
  visitados.resize(n + 1, 0);
  padres.resize(n + 1, -1);
  for (int i = 2; i < n + 1; i++) {
    int a;
    cin >> a;
    graf[a].push_back(i);
    graf[i].push_back(a);
  }
  dfs(1);
  stack<int> pila;
  int fin = n;
  while (fin != -1) {
    pila.push(fin);
    fin = padres[fin];
  }
  while (!pila.empty()) {
    cout << pila.top() << " ";
    pila.pop();
  }
  return 0;
}
