Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are $100$ dogs in the school. $\bullet$ $62$ have blue ribbons, $55$ have green ribbons, and $63$ have white ribbons. $\bullet$ $32$ have a blue ribbon and a green ribbon; $31$ have a green ribbon and a white ribbon; $38$ have a blue ribbon and a white ribbon. $\bullet$ $16$ have all three ribbons. How many dogs have not learned any tricks?
