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 small jumps.
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.
The input file will contain one or more test cases.
The first line of each test case will contain the number of stones n
The next n
lines each contain two integers
(0 ≤ xi
representing the coordinates of stone #i
Stone #1 is Freddy's stone, stone #2 is Fiona's stone, the other n
stones are unoccupied.
There's a blank line following each test case.
Input is terminated by a value of zero (0) for n
For each test case, print a line saying "Scenario #x
" and a line
saying "Frog Distance = y
" where x
is replaced by the test
case number (they are numbered from 1) and y
is replaced by the
appropriate real number, printed to three decimals.
Put a blank line after each test case, even after the last one.
Frog Distance = 5.000
Frog Distance = 1.414