Freddy Frog is sitting on a stone in the middle of a lake. Suddenly he notices
Fiona Frog who is sitting on another stone. He plans to visit her, but since the
water is dirty and full of tourists' sunscreen, he wants to avoid swimming and
instead reach her by jumping.
Unfortunately Fiona's stone is out of his jump range. Therefore Freddy considers
to use other stones as intermediate stops and reach her by a sequence of several
To execute a given sequence of jumps, a frog's jump range obviously must be at
least as long as the longest jump occuring in the sequence.
The frog distance (humans also call it minimax distance) between two stones therefore
is defined as the minimum necessary jump range over all possible paths between
the two stones.
You are given the coordinates of Freddy's stone, Fiona's stone and all other
stones in the lake. Your job is to compute the frog distance between Freddy's
and Fiona's stone.