Advanced Programming, Jan-Apr 2015
                          Assignment 7
                         22 April, 2015
                         Due 3 May, 2015

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NOTE: The usual rules apply about file names for submitting your
      assignment.
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Filename: sequences.py

                       Dividing Sequences

(IARCS OPC Archive, K Narayan Kumar, CMI)

This problem is about sequences of positive integers
a[1],a[2],...,a[N]. A subsequence of a sequence is anything
obtained by dropping some of the elements. For example, 3,7,11,3
is a subsequence of 6,3,11,5,7,4,3,11,5,3 , but 3,3,7 is not a
subsequence of 6,3,11,5,7,4,3,11,5,3 .

A fully dividing sequence is a sequence a[1],a[2],...,a[N] where
a[i] divides a[j] whenever i < j. For example, 3,15,60,720 is a
fully dividing sequence.

Given a sequence of integers your aim is to find the length of
the longest fully dividing subsequence of this sequence.

Consider the sequence 2,3,7,8,14,39,145,76,320.

It has a fully dividing sequence of length 3, namely 2,8,320, but
none of length 4 or greater.

Consider the sequence 2,11,16,12,36,60,71,17,29,144,288,129,432,993 .

It has two fully dividing subsequences of length 5,

* 2,11,16,12,36,60,71,17,29,144,288,129,432,993 and

* 2,11,16,12,36,60,71,17,29,144,288,129,432,993

and none of length 6 or greater.

Input format

The first line of input contains a single positive integer N
indicating the length of the input sequence. Lines 2,...,N+1
contain one integer each. The integer on line i+1 is a[i].

Output format

Your output should consist of a single integer indicating the
length of the longest fully dividing subsequence of the input
sequence.

Test Data

You may assume that N <= 10000.

Example:

Here are the inputs and outputs corresponding to the two examples
discussed above.

Sample input 1:

9
2
3
7
8
14
39
145
76
320

Sample output 1:

3

Sample input 2:

14
2
11
16
12
36
60
71
17
29
144
288
129
432
993

Sample output 2:

5

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