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 
#!/usr/bin/env python3
import atexit
import io
import sys
from collections import deque
sys.setrecursionlimit(123456)
_I_B = sys.stdin.read().splitlines()
input = iter(_I_B).__next__
_O_B = io.StringIO()
sys.stdout = _O_B

@atexit.register
def write():
    sys.__stdout__.write(_O_B.getvalue())

md=0

def depth(root,mrt,d):
    global md
    d+=1
    md=max(md,d)
    for i in mrt[root]:
        depth(i,mrt,d)

def main():
    global md
    mrt=dict()
    roots=[]
    for _ in range(int(input())):
        m=int(input())
        try:
            mrt[_+1]
        except KeyError:
            mrt[_+1]=[]
        if m==-1:
            roots.append(_+1)
        else:
            try:
                mrt[m].append(_+1)
            except KeyError:
                mrt[m]=[_+1]

    levels=0
    for root in roots:
        md=0
        depth(root,mrt,0)
        levels=max(levels,md)
    print(levels)
if __name__=='__main__':
    main()