Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a₁,a₂,...,a_n are good.

Now she is interested in good sequences. A sequence x₁,x₂,...,x_k is called good if it satisfies the following three conditions:

• The sequence is strictly increasing, i.e. x_i<x_i+1 for each i (1≤i≤k-1).
• No two adjacent elements are coprime, i.e. gcd(x_i,x_i+1)>1 for each i (1≤i≤k-1) (where gcd(p,q) denotes the greatest common divisor of the integers p and q).
• All elements of the sequence are good integers.

Find the length of the longest good sequence.

The input consists of two lines. The first line contains a single integer n (1≤n≤10⁵) − the number of good integers. The second line contains a single-space separated list of good integers a₁,a₂,...,a_n in strictly increasing order (1≤a_i≤10⁵;a_i<a_i+1).

Print a single integer − the length of the longest good sequence.