201364: [AtCoder]ARC136 E - Non-coprime DAG

Problem Statement

We have a directed graph $G$ with $N$ vertices numbered $1$ to $N$.

Between two vertices $i,j$ ($1 \leq i,j \leq N$, $i \neq j$), there is an edge $i \to j$ if and only if both of the following conditions are satisfied.

• $i<j$
• $\mathrm{gcd}(i,j)>1$

Additionally, each vertex has an associated value: the value of Vertex $i$ is $A_i$.

Consider choosing a set $s$ of vertices so that the following condition is satisfied.

• For every pair $(x,y)$ ($x<y$) of different vertices in $s$, $y$ is unreachable from $x$ in $G$.

Find the maximum possible total value of vertices in $s$.

Constraints

• $1 \leq N \leq 10^6$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the answer.

Sample Input 1

6
1 1 1 1 1 1

Sample Output 1

4

We should choose $s=\{1,2,3,5\}$.

Sample Input 2

6
1 2 1 3 1 6

Sample Output 2

8

We should choose $s=\{1,5,6\}$.

Sample Input 3

20
40 39 31 54 27 31 80 3 62 66 15 72 21 38 74 49 15 24 44 3

Sample Output 3

343