Counting Pythagorean Triples

A Pythagorean triple is a set of three positive integers a, b, and c that satisfy $a^2 + b^2 = c^2$.

A Pythagorean triple is a primitive Pythagorean triple (PPT) when a, b, and c have no common factor.

Write a program that takes a positive integer n and counts the following.

1. The number of different PPTs where n is the hypotenuse (c)
2. The number of non-primitive Pythagorean triples where n is the hypotenuse (c)
3. The number of different PPTs where n is one of the legs (a or b)
4. The number of non-primitive Pythagorean triples where n is one of the legs (a or b)

The triples a, b, c and b, a, c are the same, so each is counted once. A non-primitive Pythagorean triple is a Pythagorean triple that is not a PPT.

For n = 65, the cases for each item are as follows.

1. 33, 56, 65; 63, 16, 65
2. 39, 52, 65; 25, 60, 65
3. 65, 72, 97; 65, 2112, 2113
4. 65, 420, 425; 65, 156, 169

The input is a single line containing one non-negative decimal integer n (3 ≤ n ≤ 2500).

The output is one line containing four decimal integers.

The first is the number of different PPTs where n is the hypotenuse (c).

The second is the number of non-primitive Pythagorean triples where n is the hypotenuse (c).

The third is the number of different PPTs where n is one of the legs (a or b).

The fourth is the number of non-primitive Pythagorean triples where n is one of the legs (a or b).