Need help with Python code with best performance code T$3$

You are given an array $A$ of $N$ positive integers.

Consider the following operation: remove one element from A and compute the product of all the remaining array elements. If there is only one element remaining in the array, the product is equal to that element.

For example, if $A=[9,16,4],$ we can:

remove $9$ and get a product equal to $(164)=64$;

remove $16$ and get a product of $36$ ;

remove $4$ and get a product of $144.$

As seen in the example above, the product might change depending on which element we remove.

Write a function:

def solution $(A)$

that, given an array $A$ of $N$ integers, returns the number of different products that can be obtained by removing exactly one element from $A.$

Examples:

Given $A=[9,16,4],$ the function should return $3.$ As explained above, the achievable products are $64,36$ and $144.$

Given $A=[3,4,2,3,1],$ the function should return $4.$

Given $A=[1000000000,100000000],$ the function should return $1.$

Write an efficient algorithm for the following assumptions:

$N$ is an integer within the range $2.\mathrm{.}100,000$;

each element of array $A$ is an integer within the range $1.\mathrm{.}1,000,000,000.$