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

Now she is interested in good sequences. A sequence x1,x2,...,xk is called good if it satisfies the following three conditions:
The sequence is strictly increasing, i.e. xi \lt xi+1 for each i (1 \le i \le k-1). No two adjacent elements are coprime, i.e. gcd(xi,xi+1) \gt 1 for each i (1 \le i \le 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 \le n \le 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 \le ai \le 105;ai \lt ai+1).

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

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.