github.com/captn3m0/codechef.git

---
{"languages_supported":{"0":"NA"},"title":"COOKOFF2","category":"NA","old_version":true,"problem_code":"COOKOFF2","tags":{"0":"NA"},"layout":"problem"}
---

<h3> All submissions for this problem are available. </h3><p>Chef is planning a grand cooking tournament for aspiring chefs in the region.
The competition progresses with a number of one-on-one elimination rounds until only one chef remains.
For each round, two chefs are chosen at random for a cook-off.
The loser of the cook-off is elimited, while the winner moves on.
Additionally, each chef begins with a positive number of prize tokens
(some chefs begin with more than others, based on their performance in a qualification round).
The winner of each cook-off receives all of the loser's prize tokens, and the loser is
awarded a prize based on the number of prize tokens he/she had accrued.</p>

<p>The final cook-off always receives the most publicity.
Your task it to compute the expected difference between the number of prize tokens of the final two
competitors before the final cook-off.
You will be given the number of tokens each chef begins with.</p>

<h3>Input</h3>
<p>Input begins with an integer T, the number of test cases (at most 50).
Each test case consists of a single line, beginning with an integer C,
the number of chefs in the competition, followed by C positive integers each describing the number
of prize tokens a chef begins with.
The total number of prize tokens among all chefs will be between 1 and 100, inclusive.</p>

<h3>Output</h3>
<p>For each test case, output the expected difference in prize tokens, rounded to 6 places
after the decimal point.</p>

<h3>Sample Input</h3>
<pre>3
3 1 1 1
3 1 1 2
4 10 10 10 30
</pre>

<h3>Sample Output</h3>
<pre>1.000000
1.333333
26.666667
</pre>