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;
const long long int MOD = 1e9 + 7;
long long int mod(long long int x) { return (x % MOD + MOD) % MOD; }
struct Node {
  long long int data;
  Node* parent = NULL;
};
Node* createNode(long long int data) {
  Node* node = new Node();
  node->data = data;
  return node;
}
void solve() {
  long long int n;
  cin >> n;
  vector<Node*> nodes;
  nodes.push_back(createNode(1));
  for (long long int i = 2; i < n + 1; i++) {
    long long int data;
    cin >> data;
    Node* node = createNode(i);
    node->parent = nodes[data - 1];
    nodes.push_back(node);
  }
  Node* curr = *(nodes.end() - 1);
  deque<long long int> ans;
  ans.push_front(curr->data);
  curr = curr->parent;
  while (curr != NULL) {
    ans.push_front(curr->data);
    curr = curr->parent;
  }
  for (auto i : ans) {
    cout << i << " ";
  }
  cout << endl;
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
