- Let $a$ be the hypotenuse of a right angled triangle; with other two sides being $5$ and $12$ respectively.
- Let $b$ be the sum of all positive integers which cannot be the sides of a integer-sided right angled triangle.
- Let $c$ be the greatest common divisor of all possible values of $xyz$, where $x$, $y$, and $z$ are the integral sides of a right angled triangle subject to $x+y+z \ge 100$.
- Let $d$ be the number of different integer-sided right-angled triangles with one of the sides equal to $385$.

Determine $a+b+c+d$.

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