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 int INF = 1000000;
vector<int> adj[200001];
int dist[200001];
int prevv[200001];
int n;
void bfs(int x);
vector<int> getPath(int from, int to);
int main() {
  cin >> n;
  for (int i = 2; i <= n; i++) {
    int sk;
    cin >> sk;
    adj[i].push_back(sk);
    adj[sk].push_back(i);
  }
  bfs(1);
  return 0;
}
void bfs(int x) {
  for (int i = 1; i <= n; i++) {
    prevv[i] = -1;
    dist[i] = INF;
  }
  queue<int> q;
  dist[x] = 0;
  q.push(x);
  while (!q.empty()) {
    int s = q.front();
    q.pop();
    for (int u : adj[s]) {
      if (dist[u] == INF) {
        dist[u] = dist[s] + 1;
        prevv[u] = s;
        q.push(u);
      }
    }
  }
  vector<int> path = getPath(1, n);
  for (int i : path) cout << i << " ";
}
vector<int> getPath(int from, int to) {
  vector<int> path;
  int curr = to;
  while (curr != -1) {
    path.push_back(curr);
    curr = prevv[curr];
  }
  sort(path.begin(), path.end());
  return path;
}
