## LOOPEXP - Loop Expectation

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

## Code Examples

### #1 Code Example with Python Programming

```Code - Python Programming```

``````f = [0] * 100001
for i in range (1, 100001):
f[i] = f[i - 1] + 1 / i

T = int(input())
for i in range(T):
N = int(input())
print("%.14f" % f[N])``````
Copy The Code &

Input

cmd
1
2

Output

cmd
1.5