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>
typedef struct _ {
  int id;
  struct _* next;
} Node;
Node** list;
int n, a, ans[200005];
void find(int start, int pre) {
  for (Node* it = list[start]; it; it = it->next) {
    if (start == n) {
      for (int i = 1; i < n; i++)
        if (ans[i]) printf(" %d", i);
      return;
    }
    if (it->id == pre) continue;
    ans[it->id] = 1;
    find(it->id, start);
    ans[it->id] = 0;
  }
}
int main() {
  scanf("%d", &n);
  list = (Node**)malloc(sizeof(Node*) * (n + 1));
  for (int i = 1; i <= n; i++) list[i] = NULL;
  for (int i = 2; i <= n; i++) {
    scanf("%d", &a);
    Node* tmp = list[a];
    list[a] = (Node*)malloc(sizeof(Node));
    list[a]->id = i;
    list[a]->next = tmp;
    tmp = list[i];
    list[i] = (Node*)malloc(sizeof(Node));
    list[i]->id = a;
    list[i]->next = tmp;
  }
  printf("1");
  find(1, n);
  printf(" %d", n);
  for (int i = 1; i <= n; i++) {
    while (list[i]) {
      Node* del = list[i];
      list[i] = list[i]->next;
      free(del);
    }
  }
  free(list);
  return 0;
}
