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 N = 2e5 + 10;
inline int read() {
  int s = 0, b = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') b = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') s = s * 10 + c - '0', c = getchar();
  return s * b;
}
int n, now, l, i, fa[N], a[N];
int main() {
  n = read();
  now = n;
  for (i = 2; i <= n; i++) fa[i] = read();
  do a[++l] = now, now = fa[now];
  while (now != 1);
  printf("1 ");
  for (i = l; i >= 1; i--) printf("%d ", a[i]);
  return 0;
}
