# One Person Game

Time Limit: Java: 1000 ms / Others: 1000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB

## Description

There is a very simple and interesting one-person game. You have 3 dice, namely Die1, Die2 and Die3. Die1 has K1 faces. Die2 has K2 faces. Die3 has K3 faces. All the dice are fair dice, so the probability of rolling each value, 1 to K1, K2, K3 is exactly 1 / K1, 1 / K2 and 1 / K3. You have a counter, and the game is played as follow:

• Set the counter to 0 at first.
• Roll the 3 dice simultaneously. If the up-facing number of Die1 is a, the up-facing number of Die2 is b and the up-facing number of Die3 is c, set the counter to 0. Otherwise, add the counter by the total value of the 3 up-facing numbers.
• If the counter's number is still not greater than n, 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 integer T (0 < T <= 300) indicating the number of test cases. Then T test cases follow. Each test case is a line contains 7 non-negative integers n, K1, K2, K3, a, b, c (0 <= n <= 500, 1 < K1, K2, K3 <= 6, 1 <= a <= K1, 1 <= b <= K2, 1 <= c <= K3).

## 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

None

## Source

The 7th Zhejiang Provincial Collegiate Progra