ZOJ3329One Person Game(循环型 数学期望)

There is a very simple and interesting one-person game. You have 3 dice, namelyDie1,Die2andDie3.Die1hasK₁faces.Die2hasK₂faces.Die3hasK₃faces. All the dice are fair dice, so the probability of rolling each value, 1 toK₁,K₂,K₃is exactly 1 /K₁, 1 /K₂and 1 /K₃. You have a counter, and the game is played as follow:

1. Set the counter to 0 at first.
2. Roll the 3 dice simultaneously. If the up-facing number ofDie1isa, the up-facing number ofDie2isband the up-facing number ofDie3isc, set the counter to 0. Otherwise, add the counter by the total value of the 3 up-facing numbers.
3. If the counter's number is still not greater thann, go to step 2. Otherwise the game is ended.

Calculate the expectation of the number of times that you cast dice before the end of the game.

Input

There are multiple test cases. The first line of input is an integerT(0 <T<= 300) indicating the number of test cases. ThenTtest cases follow. Each test case is a line contains 7 non-negative integersn,K₁,K₂,K₃,a,b,c(0 <=n<= 500, 1 <K₁,K₂,K₃<= 6, 1 <=a<=K₁, 1 <=b<=K₂, 1 <=c<=K₃).

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Output

For each test case, output the answer in a single line. A relative error of 1e-8 will be accepted.

Sample Input

2
0 2 2 2 1 1 1
0 6 6 6 1 1 1

Sample Output

1.142857142857143
1.004651162790698

和之前Maze一个题型