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.