Let $N$ be the number of ordered triples $(A,B,C)$ of integers satisfying the conditions 
(a) $0\le A<B<C\le99$, 
(b) there exist integers $a$, $b$, and $c$, and prime $p$ where $0\le b<a<c<p$, 
(c) $p$ divides $A-a$, $B-b$, and $C-c$, and 
(d) each ordered triple $(A,B,C)$ and each ordered triple $(b,a,c)$ form arithmetic sequences. Find $N$.