A program consists of two nested loops, with a single branch instruction at the end of each loop and no other branch anywhere. The outer loop is executed $50$ times and the inner loop $20$ times. Determine the accuracy of the following three branch prediction strategies: $($a$)$ always predict not taken. $($b$)$ use $1$ bit of history and the initial prediction is not taken, $($c$)$ use $2$ bits of history assuming that the predictor starts off in the bottom left state from $$predict not taken$$ with $$not taken$$ self loop