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.