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