For $1<=$ i $<=$ N $,$ let xi in R$2$ be a two$-$dimensional input, and yi in $\{1,+1\}$ the binary label for xi$.($a$)$ Describe, in both words and with a concrete example, when the perceptron algorithm would be guaranteed to converge $($find an optimal solution to the training set$).$ For the concrete example, give N $>=5$ data points $\{($xi$,$ yi$)\}$ for which the perceptron algorithm would converge.