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 
from collections import defaultdict 
class Main:
	def __init__(self):
		self.x=defaultdict(list)
	def addition(self,a,b):
		self.x[a].append(b)
	def f1(self,start,n,distance,visited):
		# visited=[0]*n
		q=[]
		q.append(start)
		visited[start]=1
		distance[start]=1
		while q:
			start=q.pop(0)
			# print(start," ")
			for i in self.x[start]:
				# if(visited[i]==0):
				q.append(i)
				visited[i]=1
				# print(distance[start]+1,"66666",distance[i])
				if(distance[start]+1>distance[i]):
					distance[i]=distance[start]+1
n=int(input())
g=Main()
for i in range(n):
	u=int(input())-1
	if(u!=-2):
		g.addition(u, i)
distance=[0]*n
visited=[0]*n
for i in range(n):
	if(visited[i]==0):
		g.f1(i,n,distance,visited)
		# print(i," ",distance)
# print(distance)
print(max(distance))


