## FAVDICE - Favorite Dice

no tags

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```

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <iostream>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <sstream>
#include <map>

#define s(t) scanf("%d",&t);

using namespace std;

int main(){
int t;
s(t);
while(t--){
int n;
s(n);
double ans=0;
for(int i=1;i<=n;i++){
ans+=static_cast<double>(n)/i;
}
printf("%.2lf\n",ans);
}
return 0;
}``````
Copy The Code &

Input

cmd
2
1
12

Output

cmd
1.00
37.24

### #2 Code Example with Java Programming

```Code - Java Programming```

``````#include<stdio.h>

int main()
{
int t,n,i;
float s;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
s=0;
for(i=1;i<=n;i++)
s= s+ (float)1/(i);
s=(float)(s*n);
printf("%.2f\n",s);
}

return 0;
}

``````
Copy The Code &

Input

cmd
2
1
12

Output

cmd
1.00
37.24