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 
# aproach = disjoint-set

def binary_search(s,a):
    i=0
    j=len(s)-1
    while i<=j :
        mid = (i+j)//2
        if s[mid] == a :
            return(True)
        elif s[mid] > a :
            j=mid-1
        else:
            i=mid+1
    return False

n=int(input())

supervisors = [i for i  in range(1,n+1)]

s = [[] for i in range(n+1)]

def add(a,empl):
    s[a].append(empl)
    if binary_search(supervisors,empl) :
        supervisors.remove(empl)

def find_height(a): # give it a root to find the maximum height ot it
    g=1
    p=0
    for i in s[a]:
        p=max(find_height(i),p)
    g+=p
    return(g)


# reading the input

for i in range(1,n+1):
    a=int(input())
    if a!=-1 :
        add(a,i)

# finding the maximum height

ans=-10

for i in supervisors:
    ans=max(ans,find_height(i))

print(ans)