Sabya is writing code to output a random number between and inclusive. The code can output different integers in the interval with different probabilities so that the sum of the probabilities is equal to .
For evaluation, the code is run twice. If the output in both cases are different, his score is equal to the sum of the outputs. Otherwise, his score is equal to .
Sabya is very intelligent, and he writes code that maximizes his expected score. Find the expected score. Output the ratio of the expected score to the maximum possible score. The maximum possible score is .
Input Format
The first line contains : the number of test cases.
The next lines each contain a single integer, .
Output Format
Output lines: the ratio in each case.
The answer is considered correct if the absolute error is less than .
Constraints
Sample Input
3
1
2
3
Sample Output
0.00000000000
0.50000000000
0.54545454545
Explanation
In the first case, the output is always both times.
In the second case, and are generated with the probability of and
In the third case, , and are generated with the probability of , and , respectively.