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;
template <typename T>
inline void read(T &dig) {
  dig = 0;
  bool flag = false;
  char c = getchar();
  while (!isdigit(c) && c != '-') c = getchar();
  if (c == '-') flag = true, c = getchar();
  while (isdigit(c)) dig = dig * 10 + c - '0', c = getchar();
  if (flag) dig = -dig;
}
const int MAXN = (int)2e5 + 5;
struct Tree {
  int father;
  int id;
};
Tree tree[MAXN];
int n, top = 0, a;
int stack1[MAXN];
inline void init() { read(n); }
inline void solve() {
  tree[1].father = -1;
  for (register int i = (2); i <= (n); ++i) {
    read(a);
    tree[i].id = i;
    tree[i].father = a;
  }
  int curr = n;
  while (tree[curr].father != -1) {
    stack1[++top] = tree[curr].id;
    curr = tree[curr].father;
  }
  printf("1 ");
  for (register int i = (top); i >= (1); --i) printf("%d ", stack1[i]);
}
int main() {
  init();
  solve();
  return 0;
}
