## Algorithm

Problem Name: beecrowd | 2161

# Square Root of 10

By M.C. Pinto, UNILA Brazil

Timelimit: 1

The method of periodic continued fractions is one of the many ways to calculate the square root of a natural number. This method uses as denominator a repetition for fractions. This repetition can be done by a fixed number of times.

For example, by repeating 2 times the continued fraction to calculate the square root of 10, we have the following equation.

Your task is to calculate the approximate value of square root of 10 given the number N of repetitions.

## Input

The input is a natural number N (0 ≤ N ≤ 100) that indicates the quantity of denominator repetitions in the continued fraction.

## Output

The output is the approximate value of the square root with 10 decimal places.

 Input Samples Output Samples 0 3.0000000000

 1 3.16667

 5 3.16228

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

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

int main(void)
{
int n;
double ans=0.0;
scanf("%i", &n);

while(n)
{
ans+=6.0;
ans=1.0/ans;
--n;
}
ans+=3.0;

printf("%.10lf\n", ans);
return 0;
}
``````
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Output

cmd
3.0000000000

### #2 Code Example with C++ Programming

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

``````
#include <bits/stdc++.h>
using namespace std;

int main()
{
int n;
double calc = 0;
cin >> n;
while(n--){
calc+=6;
calc = 1/calc;
}
cout << fixed << setprecision(10) << 3+calc << endl;

return 0;
}
``````
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Output

cmd
3.0000000000

### #3 Code Example with Javascript Programming

```Code - Javascript Programming```

``start coding...``
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Output

cmd
3.0000000000

### #4 Code Example with Python Programming

```Code - Python Programming```

``````
def r10(n):
if n == 0:
return 6
x = 6+1/r10(n-1)
return x

n = int(input())
x = r10(n)-3
print('%.10f' % x)
``````
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Output

cmd
3.0000000000