Consider the following dataset with six examples: $($a$)$ For a new testing example, $\backslash ($ x$\_\{1\}=0\mathrm{.}0,$ x$\_\{2\}=0\mathrm{.}0,$ x$\_\{3\}=0\mathrm{.}0,$ x$\_\{4\}=0\mathrm{.}0\backslash ),$ write the distance to each of the training examples and indicate the prediction made by $1-$NN and $3-$NN using Euclidean distance. $(6$ points$)($b$)$ For a new testing example, $\backslash ($ x$\_\{1\}=0\mathrm{.}0,$ x$\_\{2\}=0\mathrm{.}0,$ x$\_\{3\}=0\mathrm{.}0,$ x$\_\{4\}=0\mathrm{.}0\backslash ),$ write the distance to each of the training examples and indicate the prediction made by $1-$NN and $3-$NN using Manhattan distance. $(6$ points$)($c$)$ What is the Leave$-$One$-$Out$-$Cross$-$Validation $($LOOCV$)$ error rate of $1-$NN using Manhattan distance on this dataset? Indicate which examples $($if any$)$ contribute to the error rate. $(6$ points$)$