FAVORITE DICE

SPOJ Problem Set (classical)

1026. Favorite Dice
Problem code: FAVDICE



BuggyD loves to carry his favorite die around. Perhaps you wonder why it's his favorite? Well, his die is magical and can be transformed into an N-sided unbiased die with the push of a button. Now BuggyD wants to learn more about his die, so he raises a question:

What is the expected number of throws of his die while it has N sides so that each number is rolled at least once?

Input

The first line of the input contains an integer t, the number of test cases. t test cases follow.

Each test case consists of a single line containing a single integer N (1 <= N <= 1000) - the number of sides on BuggyD's die.

Output

For each test case, print one line containing the expected number of times BuggyD needs to throw his N-sided die so that each number appears at least once. The expected number must be accurate to 2 decimal digits.

Example

Input:
2
1
12

Output:
1.00
37.24

SOLUTION---



#include
int main()
{
    int t,num,i;
    scanf("%d",&t);
    double ans;
    while(t--)
    {
        ans=0.0;
        scanf("%d",&num);
        double k=num;
        for(i=num;i>=1;i--)
        {
            ans+=num/k;
            k=k-1;
        }
        printf("%.2lf\n",ans);
    }
    return 0;
    
}