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;
vector<bool> vis;
vector<int> v[200001];
int parent[200001];
vector<int> ans;
void bfs(int n, int p) {
  int h;
  queue<int> q;
  q.push(n);
  vis[n] = true;
  parent[1] = 0;
  while (!q.empty()) {
    h = q.front();
    q.pop();
    for (auto i = v[h].begin(); i != v[h].end(); i++) {
      if (!vis[*i]) {
        q.push(*i);
        parent[*i] = h;
        vis[*i] = true;
      }
    }
  }
  int temp = p;
  while (temp >= 1) {
    ans.push_back(temp);
    temp = parent[temp];
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int i, n, edge, a, b;
  cin >> n;
  vis.assign(200001, false);
  for (i = 2; i <= n; i++) {
    cin >> a;
    v[a].push_back(i);
  }
  bfs(1, n);
  for (i = ans.size() - 1; i >= 0; i--) cout << ans[i] << " ";
}
