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;
int main() {
  int n, p;
  cin >> n;
  vector<vector<int> > adj(n);
  for (int i = int(1); i < int(n); i++) {
    cin >> p;
    adj[i].push_back(p - 1);
    adj[p - 1].push_back(i);
  }
  vector<int> anterior(n, -1);
  vector<bool> visitado(n, false);
  queue<int> q;
  visitado[0] = true;
  q.push(0);
  while (!q.empty()) {
    int nodo = q.front();
    q.pop();
    for (int vecino : adj[nodo]) {
      if (visitado[vecino]) continue;
      visitado[vecino] = true;
      q.push(vecino);
      anterior[vecino] = nodo;
    }
  }
  stack<int> camino;
  int actual = n - 1;
  while (actual != -1) {
    camino.push(actual);
    actual = anterior[actual];
  }
  while (!camino.empty()) {
    cout << camino.top() + 1 << " ";
    camino.pop();
  }
  return 0;
}
