B. Good Sequences
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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 a 1, a 2, ..., a n in strictly increasing order (1 ≤ a i ≤ 105a i < a i + 1).

Output

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

Examples
Input
5
2 3 4 6 9
Output
4
Input
9
1 2 3 5 6 7 8 9 10
Output
4
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.