CF264B.Good Sequences

普及/提高-

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题目描述

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.

输入格式

The input consists of two lines. The first line contains a single integer $n$ ( $1<=n<=10^{5}$ ) — 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}<=10^{5}; a_{i}<a_{i+1} ).

输出格式

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

输入输出样例

输入#1
```
5
2 3 4 6 9
```
输出#1
```
4
```
输入#2
```
9
1 2 3 5 6 7 8 9 10
```
输出#2
```
4
```

说明/提示

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.

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