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A. Party

time limit per test

memory limit per test

input

output

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

  • Ais the immediate manager of employeeB
  • Bhas an immediate manager employeeCsuch that employeeAis the superior of employeeC.

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.

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

n (1 ≤ n ≤ 2000) — the number of employees.

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.

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


求树的最大深度，用并查集，不用压缩路径。

#include<cstdio>
#include<algorithm>
using namespace std;
int main()
{
    int n;
    int a[2005];
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    int ans=0,temp;
    for(int i=1;i<=n;i++)
    {
        temp=0;
        for(int j=i;j<=n&&j!=-1;j=a[j])
            temp++;
        ans=max(ans,temp);
    }
    printf("%d\n",ans);
    return 0;
}