Problem:
Score : 100 points

Problem Statement

Given is an integer N.

Takahashi chooses an integer a from the positive integers not greater than N with equal probability.

Find the probability that a is odd.

Constraints

1 \leq N \leq 100

Input

Input is given from Standard Input in the following format:

N

Output

Print the probability that a is odd.
Your output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-6}.

Sample Input 1

4

Sample Output 1

0.5000000000

There are four positive integers not greater than 4: 1, 2, 3, and 4. Among them, we have two odd numbers: 1 and 3. Thus, the answer is \frac{2}{4} = 0.5.

Sample Input 2

5

Sample Output 2

0.6000000000

Sample Input 3

1

Sample Output 3

1.0000000000

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a,b;
ll gcd(ll a,ll b)
{
    if(!b)
        return a;
    else
        return gcd(b,a%b);
}
int main()
{
    cin>>a>>b;
    ll res = gcd(a,b);
    ll ans = 0;
    for(ll i=2;i*i<res;i++)
    {
        if(res%i==0)
        {
            ans++;
            while(res%i==0)
                res /= i;
        }
    }
    if(res>1)
        ans++;
    cout<<++ans<<endl;
}