# Problem 311: Biclinic Integral Quadrilaterals
ABCD is a convex, integer sided quadrilateral with 1 ≤ AB < BC <
CD < AD. BD has integer length. O is the midpoint of BD. AO has
integer length. We'll call ABCD a biclinic integral quadrilateral if AO
= CO ≤ BO = DO. For example, the following quadrilateral is a biclinic
integral quadrilateral: AB = 19, BC = 29, CD = 37, AD = 43, BD = 48 and
AO = CO = 23. Let B(N) be the number of distinct biclinic integral
quadrilaterals ABCD that satisfy AB2+BC2+CD2+AD2 ≤ N. We can verify that
B(10 000) = 49 and B(1 000 000) = 38239. Find B(10 000 000 000).