Good Sequences

2000ms

262144K

Description:

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.

Input:

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).

Output:

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

Sample Input:

5
2 3 4 6 9

Sample Output:

Sample Input:

9
1 2 3 5 6 7 8 9 10

Sample Output:

Note:

In the first example, the following sequences are examples of good sequences: [2; 4; 6; 9], [2; 4; 6], [3; 9], [6]. The length of the longest good sequence is 4.

Informação

Provedor Codeforces

Código CF264B