## Algorithm

Problem Name: beecrowd | 2159

# Approximate Number of Primes

By M.C. Pinto, UNILA Brazil

Timelimit: 1

Schoenfeld and Rosser published a paper in 1962 describing a minimum and a maximum value to the quantity of prime numbers up to n, for n ≥ 17. This quantity is represented by the function (n) and the inequality is shown below.

Your task is, given a natural number n, to compute the interval's minimum and maximum values to the approximate number of primes up to n.

## Input

The input is a natural number n (17 ≤ n ≤ 109).

## Output

The output is given as two values P and M with 1 decimal place each, such that P < (n) < M according to the given inequality above. These two values have one blank space between them.

 Input Samples Output Samples 17 6.0 7.5

 50 12.8 16.0

 100 21.7 27.3

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

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

int main()
{
double n, ans1, ans2;
scanf("%lf", &n);
ans1 = n/log(n);
ans2 = (1.25506)*(n/log(n));
printf("%.1lf %.1lf\n", ans1, ans2);
return 0;
}
``````
Copy The Code &

Input

cmd
17

Output

cmd
6.0 7.5

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

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

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

int main()
{
int n;
double a,b;
while(scanf("%d",&n)!=EOF){
a=n/log(n);
b=1.25506*n/log(n);
printf("%.1lf %.1lf\n",a,b);
}
return 0;
}
``````
Copy The Code &

Input

cmd
17

Output

cmd
6.0 7.5

### #3 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
var lines = input.split('\n');
var prompt = function(texto) { return lines.shift();};
const N = parseInt(prompt());

var P = (N / Math.log(N)).toFixed(1);
var M = ((1.25506 * N) / Math.log(N)).toFixed(1);

console.log(P + " " + M);
``````
Copy The Code &

Input

cmd
17

Output

cmd
6.0 7.5