human
What is a Python program to print a single integer denoting the minimum number of groups that will be formed in the party given the following:
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 
Solve the task in PYTHON3.
assistant
#Here is Python program to print a single integer denoting the minimum number of groups that will be formed in the party.

import sys
sys.setrecursionlimit(10**5)
def res():
    def re(x,v,y):
        v[y]=True
        t=0
        for j in x[y]:
            t=max(t,1+(re(x,v,j)))
        return t
    n=int(input())
    x={}
    v={}
    for i in range(1,n+1):
        x[i]=[]
        v[i]=False
    for i in range(1,n+1):
        t=int(input())
        if t==-1:
            continue
        else:
            
            x[t].append(i)
    #print(x)
    k=0
    for i in x:
        if v[i]==False and x!=[]:
            k=max(k,re(x,v,i))
    print(k+1)
res()