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 
# python2
import sys
import os.path
from collections import deque

def bfs(node,lis1,data,record):
    que = deque() 
    que.appendleft(node)
    while len(que) !=0 :
        current = que.pop()
        #print current
        if current!=node:
            record[current] = record[data[current]]+1
        for x in lis1[current]:
            que.appendleft(x)
    return record

def main():
    if os.path.exists('input.txt'):
        input = open('input.txt', 'r').read()
    else:
        input = sys.stdin.read()
    #--------------------------------INPUT---------------------------------
    data = list(map(int, input.split()))
    lis1 =  [ [] for i,x in enumerate(data)]
    record =  [ -1 for i,x in enumerate(data)]
    for i,x in enumerate(data):
        if i ==0:
            continue
        if  x == -1:
            record[i]=1
            continue
        lis1[x].append(i)
    for i,x in enumerate(data):
        if i ==0:
            continue
        if x == -1:
            record = bfs(i,lis1,data,record)
    #print lis1
    #print record
    output = max(record)
    #-------------------------------OUTPUT----------------------------------
    if os.path.exists('output.txt'):
        open('output.txt', 'w').writelines(str(output))
    else:
        sys.stdout.write(str(output))


if __name__ == "__main__":
    main()
