$(10)(15$ points$)$ We would like to use a perceptron to train a classifier for datasets with $2$ features per point and labels $+1$ or $-1.$ Consider the following labeled training data:

$($a$)$ The perceptron weights have been initialized to w$1=2$ and w$2=-2.$ After processing the first point with the perceptron algorithm, what will be the updated values for these weights?

$($b$)$ After how many steps will the perceptron algorithm converge? Write "never" if it will never converge.

Note: one steps means processing one point. Points are processed in order and then repeated, until convergence.