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 
"""Template for Python Competitive Programmers prepared by Mayank Chaudhary aka chaudhary_19"""

# to use the print and division function of Python3
from __future__ import division, print_function

"""value of mod"""
MOD = 998244353

"""use resource"""
# import resource
# resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])

"""for factorial"""
# fact = [1]
# for i in range(1, 100005):
#     fact.append((fact[-1] * i) % MOD)
# ifact = [0] * 100005
# ifact[100004] = pow(fact[100004], MOD - 2, MOD)
# for i in range(100004, 0, -1):
#     ifact[i - 1] = (i * ifact[i]) % MOD

"""uncomment next 4 lines while doing recursion based question"""
# import threading
# threading.stack_size(2**27)
import sys

# sys.setrecursionlimit(10**6)



"""uncomment modules according to your need"""
# from bisect import bisect_left, bisect_right, insort
# import itertools
# from math import floor, ceil, sqrt
# import heapq
# from random import randint as rn
# from Queue import Queue as Q
# from collections import Counter, defaultdict

'''
def modinv(n, p):
    return pow(n, p - 2, p)
'''

"""
def ncr(n, r, p):  # for using this uncomment the lines calculating fact and ifact
    t = ((fact[n]) * ((ifact[r] * ifact[n - r]) % p)) % p
    return t
"""


def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def input(): return sys.stdin.readline().strip()


# def GCD(x, y):
#     while (y):
#         x, y = y, x % y
#     return x
#
# def lcm(x, y):
#     return (x*y)//(GCD(x, y))
#
# def get_xor(n):
#     return [n,1,n+1,0][n%4]


"""*******************************************************"""


def dfs(node, level, mydict, visited):
    visited[node] = True
    maxi = level
    for child in mydict[node]:
        if not visited[child]:
            maxi = max(maxi, dfs(child, level + 1, mydict, visited))
    return maxi

def main():

    n = int(input())
    mydict = {i : [] for i in range(1, n+1)}
    parent = {i : -1 for i in range(1, n+1)}
    for i in range(n):
        child = int(input())
        if child != -1:
            mydict[child].append(i+1)
            parent[i+1] = child
    # print(mydict)

    visited = [False]*(n+1)
    max_level = 0
    for i in range(1, n+1):
        if not visited[i] and parent[i]==-1 :
            max_level = max(max_level, dfs(i, 0, mydict, visited))

    print(max_level + 1)

""" -------- Python 2 and 3 footer by Pajenegod and c1729 ---------"""

py2 = round(0.5)
if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip

    range = xrange

import os, sys
from io import IOBase, BytesIO

BUFSIZE = 8192


class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.writable = "x" in file.mode or "w" in file.mode
        self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
        s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
        self.seek((self.tell(), self.seek(0, 2), super(FastIO, self).write(s))[0])
        return s

    def read(self):
        while self._fill(): pass
        return super(FastIO, self).read()

    def readline(self):
        while self.newlines == 0:
            s = self._fill();
            self.newlines = s.count(b"\n") + (not s)
        self.newlines -= 1
        return super(FastIO, self).readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.getvalue())
            self.truncate(0), self.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        if py2:
            self.write = self.buffer.write
            self.read = self.buffer.read
            self.readline = self.buffer.readline
        else:
            self.write = lambda s: self.buffer.write(s.encode('ascii'))
            self.read = lambda: self.buffer.read().decode('ascii')
            self.readline = lambda: self.buffer.readline().decode('ascii')


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')

""" main function"""

if __name__ == '__main__':
    main()
# threading.Thread(target=main).start()