Fermat's last theorem (3) P94857

This is another exercise about Fermat’s last theorem, which was explained in the exercise problem://problemsjutge.org:problems/p1/roura/fermat-1.pbm

Write a program that, given four natural numbers $a,b,c,d$ with $a\le b$ and $c\le d$, prints the number of solutions to the equation $$x^2 + y^2 = z^2$$ such that $a \le x \le b$ and $c \le y \le d$.

Input

Input has several cases. Each case consists of four natural numbers $a, b, c, d$ such that $a\le b$ and $c\le d$.

Output

For every case, print in a line the number of solutions to the equation $$x^2 + y^2 = z^2$$ that fulfill $a \le x \le b$ and $c \le y \le d$.