Problem3362--Good Sequences

3362: Good Sequences

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

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 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<xi+1 for each i (1≤i≤k-1).
  • No two adjacent elements are coprime, i.e. gcd(xi,xi+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,...,an in strictly increasing order (1≤ai≤105;ai<ai+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.

Source/Category

 
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