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;
bool isPrime(long long n) {
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
vector<long long> dfs(map<long long, vector<long long> > m, long long start,
                      long long target) {
  vector<long long> vect;
  if (!m[start].size()) {
    vect.push_back(LLONG_MAX);
    return vect;
  }
  long long siz = m[start].size();
  for (long long i = 0; i < siz; i++) {
    long long t = m[start][i];
    if (t == target) {
      vect.push_back(t);
      return vect;
    }
    vector<long long> temp = dfs(m, t, target);
    if (temp[0] != LLONG_MAX) {
      temp.push_back(t);
      return temp;
    }
  }
  vect.push_back(LLONG_MAX);
  return vect;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long n;
  cin >> n;
  vector<long long> vect(n);
  vector<long long> path;
  for (long long i = 1; i < n; i++) {
    cin >> vect[i];
  }
  long long k = n - 1LL;
  path.push_back(n);
  while (vect[k] != 1) {
    path.push_back(vect[k]);
    k = vect[k] - 1;
  }
  path.push_back(1);
  k = path.size() - 1;
  for (long long j = k; j >= 0; j--) {
    cout << path[j] << " ";
  }
  return 0;
}
