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;
int n, fa[200005];
template <typename Drake>
void Read(Drake &x) {
  x = 0;
  char ch = getchar();
  int f = 1;
  while (!isdigit(ch)) {
    if (ch == '-') f = -f;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  x = x * f;
}
template <typename Drake>
void write(Drake x) {
  if (x < 0) {
    x = -x;
    putchar('-');
  }
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
template <typename Drake>
void writeln(Drake x) {
  write(x);
  puts("");
}
void Init() {
  Read(n);
  for (int i = 2; i <= n; ++i) Read(fa[i]);
}
void dfs(int node) {
  if (node == 1) {
    cout << 1;
    return;
  }
  dfs(fa[node]);
  cout << " " << node;
}
int main() {
  Init();
  dfs(n);
  puts("");
  return 0;
}
