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;
long long mod = 1e9 + 7;
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
long long power(long long a, long long b) {
  if (b == 0) return 1;
  if (b == 1) return a;
  long long ans = power(a, b / 2);
  ans = (ans * ans) % mod;
  if (b & 1) ans = (ans * a) % mod;
  return ans;
}
long long vis[200001];
vector<long long> nodes;
vector<long long> v[200001];
map<long long, long long> flag;
bool dfs(long long u, long long n) {
  if (vis[u]) {
    return flag[u];
  }
  vis[u] = 1;
  if (u == n) {
    flag[u] = 1;
    return flag[u];
  }
  bool f;
  for (auto x : v[u]) {
    f = dfs(x, n);
    if (f) {
      nodes.push_back(x);
      flag[x] = 1;
      return flag[x];
    }
  }
  return 0;
}
int main() {
  fast();
  long long n;
  cin >> n;
  for (long long i = 2; i <= n; i++) {
    long long x;
    cin >> x;
    v[x].push_back(i);
  }
  dfs(1, n);
  cout << 1 << " ";
  for (long long i = nodes.size() - 1; i >= 0; i--) {
    cout << nodes[i] << " ";
  }
}
