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<long long int> edges[200005];
bool vis[200005];
long long int parent[200005];
void solve() {
  long long int n;
  cin >> n;
  for (long long int i = 2; i <= n; i++) {
    long long int p;
    cin >> p;
    edges[p].push_back(i);
    edges[i].push_back(p);
  }
  queue<long long int> q;
  long long int src = 1;
  parent[src] = -1;
  vis[src] = 1;
  q.push(src);
  while (!q.empty()) {
    long long int u = q.front();
    q.pop();
    for (auto x : edges[u]) {
      if (!vis[x]) {
        vis[x] = 1;
        parent[x] = u;
        q.push(x);
        if (x == n) {
          break;
        }
      }
    }
  }
  vector<long long int> path;
  long long int crawl = n;
  path.push_back(crawl);
  while (parent[crawl] != -1) {
    path.push_back(parent[crawl]);
    crawl = parent[crawl];
  }
  reverse(path.begin(), path.end());
  for (auto x : path) {
    cout << x << " ";
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t = 1;
  for (long long int i = 0; i < t; i++) {
    solve();
  }
  return 0;
}
