Longest Factor Chain

Problem Description

Given an array $a_1, a_2, \dots, a_n$ of length $n$, find the length of the longest factor chain. That is, find the largest $m$ and indices $p_1, p_2, \dots, p_m$ such that the $p_i$ are pairwise distinct and $a_{p_1}$ is a factor of $a_{p_2}$, $a_{p_2}$ is a factor of $a_{p_3}$, $\dots$

Note that a number is a factor of itself, and the numbers do not need to appear in order.

Input Format

The first line contains an integer $n$.

The next line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output Format

One integer — the answer.

Sample Input

6
3 7 4 2 6 8

Sample Output

3

Constraints

All data satisfy $1 \le n \le 1000$ and $1 \le a_i \le 10^9$.