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 maxn = 2e5 + 5;
int n, m, par[maxn];
vector<int> edges[maxn];
bool vis[maxn], f;
vector<int> path;
void dfs(int u, int p) {
  vis[u] = 1;
  par[u] = p;
  for (auto v : edges[u]) {
    if (!vis[v]) dfs(v, u);
  }
}
int main() {
  cin >> n;
  for (int i = 1; i < n; i++) {
    int x;
    cin >> x;
    edges[i + 1].push_back(x);
    edges[x].push_back(i + 1);
  }
  dfs(1, -1);
  int p = n;
  while (p != -1) {
    path.push_back(p);
    p = par[p];
  }
  reverse(path.begin(), path.end());
  for (auto x : path) cout << x << ' ';
  cout << endl;
  return 0;
}
