Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

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.

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 will contain one or more test cases. The first line of each test case
will contain the number of stones n (2 <= n <= 200). The next n lines
each contain two integers xi, yi (0 <= xi, yi <= 1000) representing the
coordinates of stone #i. Stone #1 is Freddy's stone, stone #2 is Fiona's stone,
the other n-2 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.

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