Chef Loves Maths

Chef was given an array $A$ of length $N$. To calculate the score of an array, he defined a two-step process: 1. Multiply all the array elements to get the product, say $P$, i.e., $A_1 \times A_2 \times ... \times A_n = P$. 2. Choose $k$ integers $[x_1, x_2, ..., x_k]$ such that $ \sum_{i=1}^{k} x_i^2 = P $. Note that it is **not** necessary to choose distinct integers. Then, the score of the arr