Swapped Distributive Law

Recently, Jeuti studied addition and multiplication and learned the distributive law. The distributive law means that for any three real numbers $a$, $b$, $c$, the equation $a \times (b + c) = (a \times b) + (a \times c)$ always holds. Jeuti then wondered whether the expression with the positions of the addition and multiplication signs swapped also holds: for any three real numbers $a$, $b$, $c$, $a + (b \times c) = (a + b) \times (a + c)$. Jeuti is still young and cannot handle large numbers, so Jeuti can only evaluate these expressions when $a$, $b$, $c$ are integers whose absolute values do not exceed $N$. Count the integer pairs $(a, b, c)$ within this range that satisfy the swapped distributive law.

The first line contains $N$, the bound on the absolute values of $a$, $b$, and $c$. $(1 \leq N \leq 3000)$

Print the number of integer triples $(a, b, c)$ that satisfy the swapped distributive law.