A company has n employees numbered from 1 to n. Each employee either has no immediate manager or exactly one immediate manager, who is another employee with a different number. An employee A is said to be the superior of another employee B if at least one of the following is true:

  * Employee A is the immediate manager of employee B
  * Employee B has an immediate manager employee C such that employee A is the superior of employee C. 



The company will not have a managerial cycle. That is, there will not exist an employee who is the superior of his/her own immediate manager.

Today the company is going to arrange a party. This involves dividing all n employees into several groups: every employee must belong to exactly one group. Furthermore, within any single group, there must not be two employees A and B such that A is the superior of B.

What is the minimum number of groups that must be formed?

Input

The first line contains integer n (1 ≤ n ≤ 2000) — the number of employees.

The next n lines contain the integers pi (1 ≤ pi ≤ n or pi = -1). Every pi denotes the immediate manager for the i-th employee. If pi is -1, that means that the i-th employee does not have an immediate manager. 

It is guaranteed, that no employee will be the immediate manager of him/herself (pi ≠ i). Also, there will be no managerial cycles.

Output

Print a single integer denoting the minimum number of groups that will be formed in the party.

Examples

Input

5
-1
1
2
1
-1


Output

3

Note

For the first example, three groups are sufficient, for example: 

  * Employee 1 
  * Employees 2 and 4 
  * Employees 3 and 5 
def geti(dic, i, cont):
	boole = False
	for e in dic[i]:
		if e in dic:
			boole = True
			geti(dic, e, cont+1)
	if not boole:
		biu.append(cont)

n = int(input())
lista = []
valores = []
dicgeral = {}

for e in range(n):
	ent = int(input())
	valores.append(ent)
	if ent == -1:
		dicgeral[e+1] = []
		lista.append(e+1)
for i in range(n):
	if valores[i] != -1:
		if valores[i] in dicgeral:
			dicgeral[valores[i]].append(i+1)
		else:
			dicgeral[valores[i]] = [i+1]
			
maior = 0

for e in lista:
	biu = []
	if len(dicgeral[e]):
		geti(dicgeral, e, 1)
		if max(biu) > maior:
			maior = max(biu)
maior += 1
print(maior)



   	   		 		 					 	 		    			