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;
long long parent[200020];
int main() {
  long long N, p;
  while (scanf("%lld", &N) == 1) {
    parent[1] = -1;
    for (long long v = 2; v <= N; v++) {
      scanf("%lld", &p);
      parent[v] = p;
    }
    vector<long long> path;
    p = N;
    while (p != -1) {
      path.push_back(p);
      p = parent[p];
    }
    for (long long i = path.size() - 1; i >= 0; i--) {
      printf("%lld", path[i]);
      if (i > 0) printf(" ");
    }
    printf("\n");
  }
  return 0;
}
