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("O3")
using namespace std;
template <class T>
T Gcd(T x, T y) {
  return y ? Gcd(y, x % y) : x;
}
template <class T>
T Lcm(T x, T y) {
  return x / Gcd(x, y) * y;
}
const long long MOD = 1000000007LL;
const int M = 5000005;
const int N = 200005;
int n, t, a[N], b[N], ed;
int main() {
  scanf("%d", &n);
  for (int i = 2; i <= n; i++) scanf("%d", &a[i]);
  t = n;
  b[++ed] = n;
  while (t != 1) {
    t = a[t];
    b[++ed] = t;
  }
  for (int i = ed; i >= 1; i--) printf("%d ", b[i]);
  return 0;
}
