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 
from collections import deque
from collections import OrderedDict
import math
 
import sys
import os
from io import BytesIO
import threading
import bisect
 
 
import heapq

#sys.stdin = open("F:\PY\\test.txt", "r")
input = lambda: sys.stdin.readline().rstrip("\r\n")


n = int(input())
ar = [0, 0]+list(map(int, input().split()))
value=n
answer = []
while value!=0:
    #print(value, end=" ")
    answer.append(value)
    value = ar[value]
answer.reverse()
for i in range(len(answer)):
    print(answer[i], end=" ")