Dividing Sequences

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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: 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: Your output should consist of a single integer indicating the length of the longest fully dividing subsequence of the input sequence. ###Constraints:  $1 \leq N \leq 10000$  $1 \leq a_i \leq 1000000000$ ###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: 5Author:  admin2 
Date Added:  17092018 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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