The number of functions f, from the set A ={x ∈ N: x^2-10 x+9 ≤ 0} to the set B ={ n^2: n ∈ N } such that f(x) ≤(x-3)^2+1, for every x ∈ A, is \ \ \…

The number of functions $\displaystyle f$, from the set $\displaystyle \mathrm{A}=\left\{x \in \mathbf{N}: x^2-10 x+9 \leq 0\right\}$ to the set $\displaystyle \mathrm{B}=\left\{\mathrm{n}^2: \mathrm{n} \in \mathbf{N}\right\}$ such that $\displaystyle f(x) \leq(x-3)^2+1$, for every $\displaystyle x \in \mathrm{~A}$, is \_\_\_\_.