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>
#pragma gcc optimize("Ofast")
using namespace std;
template <typename T>
using maxHeap = priority_queue<T, vector<T>, less<T>>;
template <typename T>
using minHeap = priority_queue<T, vector<T>, greater<T>>;
inline void input(int& _x) {
  _x = 0;
  int _tmp = 1;
  char _tc = getchar();
  while ((_tc < '0' || _tc > '9') && _tc != '-') _tc = getchar();
  if (_tc == '-') _tc = getchar(), _tmp = -1;
  while (_tc >= '0' && _tc <= '9') _x = _x * 10 + (_tc - 48), _tc = getchar();
  _x *= _tmp;
}
inline void output(int _x) {
  char _buff[20];
  int _f = 0;
  if (_x == 0) putchar('0');
  while (_x > 0) {
    _buff[_f++] = _x % 10 + '0';
    _x /= 10;
  }
  for (_f -= 1; _f >= 0; _f--) putchar(_buff[_f]);
  putchar('\n');
}
template <typename Iter>
ostream& _out(ostream& s, Iter b, Iter e) {
  s << "[";
  for (auto it = b; it != e; it++) s << (it == b ? "" : " ") << *it;
  s << "]";
  return s;
}
template <class T1, class T2>
ostream& operator<<(ostream& out, pair<T1, T2> p) {
  return out << '(' << p.first << ", " << p.second << ')';
}
template <typename T>
ostream& operator<<(ostream& s, const vector<T>& c) {
  return _out(s, c.begin(), c.end());
}
vector<int> xx, yy;
signed main() {
  int n;
  cin >> n;
  xx.push_back(0);
  for (int i = 1; i < n; i++) {
    int x;
    cin >> x;
    xx.push_back(x - 1);
  }
  int i = n - 1;
  do yy.push_back(i + 1);
  while (i = xx[i]);
  yy.push_back(1);
  reverse((yy).begin(), (yy).end());
  for (auto i : yy) cout << i << " ";
}
