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;
class node {
 public:
  vector<int> adjlist;
  bool visited = 0;
  int parent = -1;
};
int main(int argc, char const *argv[]) {
  int n;
  cin >> n;
  vector<node> v(n + 1);
  for (int i = 0; i < n - 1; i++) {
    int x;
    cin >> x;
    v[x].adjlist.push_back(i + 2);
  }
  int s = 1, d = n;
  queue<int> q;
  q.push(s);
  v[s].visited = 1;
  int flag = 0;
  while (!q.empty()) {
    int p = q.front();
    q.pop();
    for (int i = 0; i < v[p].adjlist.size(); i++) {
      int nd = v[p].adjlist[i];
      if (v[nd].visited == 0) {
        q.push(nd);
        v[nd].visited = 1;
        v[nd].parent = p;
        if (nd == d) {
          flag = 1;
        }
      }
    }
    if (flag == 1) break;
  }
  int temp = d;
  vector<int> path;
  while (v[d].parent != -1) {
    path.push_back(v[d].parent);
    d = v[d].parent;
  }
  int l = path.size();
  for (int i = l - 1; i >= 0; i--) cout << path[i] << " ";
  cout << temp << endl;
  return 0;
}
