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 
n = int(raw_input())
s = raw_input().split()
for idx,i in enumerate(s):
	s[idx] = int(i)

#print s
arr = []
arr.append(n)
temp = n-1
while s[temp-1]!=1:
	y = s[temp-1]
	arr.append(y)
	temp = y-1

arr.append(1)
arr = arr[::-1]
for i in arr:
	print (i),





def powMod(x,y,mod):
	ans = 1
	while y > 0:
		if y % 2 == 0:
			x *= x
			x %= mod
		else:
			ans *= x
			ans %= mod
	return ans