Use Java. Plz give solution with most optimized approach implement using DP if required Virtual machines

You're setting up a cloud service with $N$ virtual

machines $($VM$)$ numbered from $1$ to $N$ and $N$ types of

virtual keys $($Key$).$ Each virtual key is distributed to a

distinct virtual machine. The cloud service is fully set

up when each virtual machine meets at least one

condition.

$-V{M}_i\%Ke{y}_j==0$

$-$ Keyj$\%V{M}_i==0$

Find the total number of times the cloud service is fully

set up across all possible permutations of distributing

virtual machine keys to virtual machines

Function description

Complete the solve$()$ function. This function takes the

following parameter and returns an integer denoting

the answer to the question:

$N$ : Represents the total number of virtual

machines and virtual keys

Key: Represents the virtual key

Input format for custom testing

Note: Use this input format if you are testing against

custom input or writing code in a language where we

don't provide boilerplate code.

The first line contains an integer $N.$

The second line contains $N$ space$-$separated

integers.

Output format

Print the answer in a new line.

Constraints