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 compare {
 public:
  bool operator()(pair<int, int> x, pair<int, int> y) {
    if (x.second == y.second) {
      return x.first < y.first;
    }
    return x.second < y.second;
  }
};
int Set(int N, int pos) { return N = N | (1 << pos); }
bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<vector<int> > AdjLst;
  AdjLst.assign(n + 1, vector<int>());
  vector<int> dir(n + 1, -1);
  for (int i = 2; i <= n; i++) {
    int a;
    cin >> a;
    AdjLst[a].push_back(i);
    AdjLst[i].push_back(a);
  }
  queue<int> q;
  q.push(n);
  bool visited[n + 1];
  memset(visited, false, sizeof visited);
  visited[n] = true;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = 0; i < AdjLst[u].size(); i++) {
      if (!visited[AdjLst[u][i]]) {
        visited[AdjLst[u][i]] = true;
        dir[AdjLst[u][i]] = u;
        q.push(AdjLst[u][i]);
      }
    }
  }
  int start = 1;
  while (start != n) {
    cout << start << " ";
    start = dir[start];
  }
  cout << start << endl;
  return 0;
}
