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 argc, char *argv[]) {
  int n;
  cin >> n;
  vector<vector<int>> rou(n + 1);
  vector<int> dist(n + 1, -1);
  vector<int> rep(n + 1, -1);
  for (int i = 1; i < n; i++) {
    int a;
    cin >> a;
    rou[a].push_back(i + 1);
  }
  int ori = 1;
  dist[ori] = 0;
  queue<int> cola;
  cola.push(ori);
  while (!cola.empty()) {
    int nodo = cola.front();
    cola.pop();
    for (int i = 0; i < rou[nodo].size(); i++) {
      int ady = rou[nodo][i];
      if (dist[ady] == -1) {
        dist[ady] = dist[nodo] + 1;
        rep[ady] = nodo;
        cola.push(ady);
      }
    }
  }
  int fin = n;
  stack<int> pila;
  pila.push(fin);
  while (rep[fin] != -1) {
    pila.push(rep[fin]);
    fin = rep[fin];
  }
  while (!pila.empty()) {
    cout << pila.top() << " ";
    pila.pop();
  }
  return 0;
}
