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

Explanation

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

In the first case the if block gets executed 2 times, and in the second case the if block gets executed 1 time. So the expected value is (2 + 1) / 2 = 1.5