Equation

Let three positive integers (X), (Y), and (Z) satisfy the equation below.

[ X + Y = Z \quad (X \le Y) ]

Without restrictions there can be infinitely many solutions. For each of the following three conditions, applied independently, count how many solutions satisfy the equation.

• Condition A: (X), (Y), and (Z) are all at most (N), and they are pairwise distinct.
• Condition B: (X), (Y), and (Z) are all positive divisors of (N).
• Condition C: (X), (Y), and (Z) are all positive primes at most (N).

The conditions are not applied together. Compute the number of solutions separately for conditions A, B, and C.

The first line contains a positive integer (N).

[ 1 \le N \le 500,000 ]

Print the number of solutions under condition A on the first line.

Print the number of solutions under condition B on the second line.

Print the number of solutions under condition C on the third line.