Let N be the number of ordered triples (A, B, C) of integers satisfying the conditions

(a) 0 \leq A<B<C \leq 99,

(b) there exist integers a, b, and c, and prime p where 0 \leq 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.