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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.util.Scanner;

class Main {
  static public void main(String args[]) {
    Scanner sc = new Scanner(System.in);
    long A = sc.nextLong();
    long B = sc.nextLong();
    long gcd = gcd(A, B);
    int counter = 1;
    for(int i = 2; i < Math.max(A, B); i++) {
      if(gcd % i == 0) {
        counter++;
      }
      while(gcd % i == 0) {
        gcd /= i;
      }
    }
    System.out.println(counter);
    return;
  }

  private static long gcd(long m, long n) {
    if(m < n) {
      return gcd(n, m);
    }
    if(n == 0) {
      return m;
    }
    return gcd(n, m % n);
  }
}