Consider the following pseudo-code

int a[1..N]; 

int max = -1;

for i = 1..N:

if(a[i] > max) 

max = a[i];

Your task is to calculate the expected number of times the 'if' block of the above pseudo-code executes. The array 'a' is a random permutation of numbers from 1..N chosen uniformly at random. 

Input

First line contains t, the number of test cases. t lines follow, each containing N, the number of elements in the array.

1<= t <= 100

1<= n <=100,000

Output

For each test case, output a single decimal. Your answer should be within 10^-6 of the correct answer.

Example

Input:
1

2
Output:

1.5

Explaination :

for N=2, you can have the following two permutations: [1,2]  and [2,1] . 

for the first case the if block gets executed 2 times and for the second one the if block gets executed 1 time. So the expected 

value is (3)/2 = 1.5