Kubík went to buy a pizza. To his surprise, the pizza box was made out of recycled… punch cards!

With his eagle eye, he deciphered the program the punch cards described:

n = read_input();
ans = 0;
while(n > 0)
{
    ans = ans + 1;
    n = random() % n;
}

random() is a function which returns uniformly random non-negative integers, and % is the modulus operator.

Now he wonders what the expected value of ans would be for a given initial value of n, and he is unable to enjoy his pizza until someone computes the answer for him.

Input

The first line contains an integer 1 ≤ T ≤ 5 - the number of test cases.

Each of the next T lines contain a single integer n, where 1 ≤ n ≤ 300 000. The sum of n within an input file won't exceed 300000.

Output

Output the expected value of the variable ans – that is, the sum of v × (probability that ans will end up with value v), for all possible values v.

Your answer will be considered correct if the absolute or relative error does not exceed 10⁻⁹. Make sure to print enough decimal places.

Example

Input:

2
2
47

Output:

1.5
4.4379638417

In the first case, either random()%2 = 0 with probability 1/2, which leads to ans = 1, or random()%2 = 1 with probability 1/2, after which we certainly get random()%1 = 0, so ans = 2. Expected value of ans is therefore 1 × 1/2 + 2 × 1/2 = 1.5.