A Pythagorean triple is a set of three positive integers, $a, b$ and $c$, for which:

$$a^2 + b^2 = c^2$$

A Pythagorean triple is a Primitive Pythagorean Triple (PPT) if $a, b$ and $c$ have no common factors.

Write a program which takes as input a positive integer, $n$, and outputs a count of:

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

For the same $a, b, c$: $b, a, c$ is the “same” as $a, b, c$ (i.e it only counts once). Non-primitive Pythagorean triples are Pythagorean triples which are not PPT.

For example, in the case of $n = 65$, the following are the cases for each of the criteria above:

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

Input consists of a single line containing a single non-negative decimal integer $n, (3 ≤ n ≤ 2500)$.

There is one line of output. The single output line contains four decimal integers:
The first is the number of different PPTs in which $n$ is the hypotenuse ( $c$ ).
The second is the number of non-primitive Pythagorean triples in which $n$ is the hypotenuse ( $c$).
The third is the number of different PPTs in which $n$ is the one of the sides ( $a$ or $b$ ).
The fourth is the number of non-primitive Pythagorean triples in which $n$ is the one of the sides ($a$ or $b$).