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 
input_0 = input()
input_1 = input()

value = int(input_0)
tree = [0]
i = 0
wow = ''
for j in range(len(input_1)):
	if input_1[j] == ' ' :
		tree.append(int(wow))
		wow = ''
	elif j == len(input_1)-1:
		wow = wow + input_1[j]
		tree.append(int(wow))
	else:
		wow = wow + input_1[j]
ans = []
element = value
while element > 0:
	ans.append(element)
	element = tree[element-1]
real_ans = ''
yee = len(ans)
for j in range(yee):
	part = yee - 1 - j
	if j > 0:
		real_ans = real_ans + ' '
	real_ans = real_ans + str(ans[part])
print(real_ans)


