A group of war prisoners are trying to escape from a prison. They have thoroughly planned the escape from the prison itself, and after that they hope to find shelter in a nearby village. However, the village (marked as $B$, see picture below) and the prison (marked as $A$) are separated by a canyon which is also guarded by soldiers (marked as $S$). These soldiers sit in their pickets and rarely walk; the range of view of each soldier is limited to exactly $100$ meters. Thus, depending on the locations of soldiers, it may be possible to pass the canyon safely, keeping the distance to the closest soldier strictly larger than $100$ meters from any moment. The situation is depicted in the following picture, where the circles around $S$ indicate the range of view.
Provide an algorithm to determine if the prisoners can pass the canyon unnoticed, given the width and the length of a canyon and the coordinated of every soldier in the canyon, and assuming that soldiers do not change their locations ($Hint$: Model this as a graph, with soldiers represented by the vertices.)
