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 $*p*_{*i*}$ ($1 ≤ *p*_{*i*} ≤ *n*$ or $*p*_{*i*} =$-1). Every $*p*_{*i*}$ denotes the immediate manager for the $*i*$-th employee. If $*p*_{*i*}$ 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 ($*p*_{*i*} ≠ *i*$). 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.

Note

For the first example, three groups are sufficient, for example:

• Employee 1
• Employees 2 and 4
• Employees 3 and 5