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>
int main() {
  int n;
  std::cin >> n;
  std::stack<int> path;
  std::stack<int> routers;
  int k;
  for (int i = 0; i < n - 1; i++) {
    std::cin >> k;
    routers.push(k);
  }
  int router = n;
  int to_go = k;
  while (to_go != 1) {
    for (int i = 0; i < (router - to_go); i++) {
      routers.pop();
    }
    router = to_go;
    to_go = routers.top();
    path.push(router);
  }
  std::cout << 1 << " ";
  int r;
  while (!path.empty()) {
    r = path.top();
    path.pop();
    std::cout << r << " ";
  }
  std::cout << n << " ";
}
