A9868 | Clique in the Divisibility Graph

As you must know, the maximum clique problem in an arbitrary graph is $NP$ -hard. Nevertheless, for some graphs of specific kinds it can be solved effectively.

Just in case, let us remind you that a clique in a non-directed graph is a subset of the vertices of a graph, such that any two vertices of this subset are connected by an edge. In particular, an empty set of vertexes and a set consisting of a single vertex, are cliques.

Let's define a divisibility graph for a set of positive integers $A={a_{1},a_{2},...,a_{n}}$ as follows. The vertices of the given graph are numbers from set $A$ , and two numbers $a_{i}$ and $a_{j}$ ( $i≠j$ ) are connected by an edge if and only if either $a_{i}$ is divisible by $a_{j}$ , or $a_{j}$ is divisible by $a_{i}$ .

You are given a set of non-negative integers $A$ . Determine the size of a maximum clique in a divisibility graph for set $A$ .

The first line contains integer $n$ ( $1<=n<=10^{6}$ ), that sets the size of set $A$ .

The second line contains $n$ distinct positive integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{6}$ ) — elements of subset $A$ . The numbers in the line follow in the ascending order.

Print a single number — the maximum size of a clique in a divisibility graph for set $A$ .