Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a 1, a 2, ..., a n are good. Now she is interested in good sequences. A sequence x 1, x 2, ..., 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.

输入描述:

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, ..., an in strictly increasing order (1 ≤ ai ≤ 105; ai ai + 1).

输出描述:

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

备注:

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.