Triangles and Centres

You are given three points A,B,C all with integer coordinates. Points P,Q,R lie on the sides BC,CA and AB such that lines AP,BQ and CR are perpendicular to BC,CA and AB respectively. AP, BQ and CR meet at H(called the orthocentre of the triangle). Find a triangle XYZ (all points having integer coordinates) such that the centre of the circle passing through X,Y,Z is H. Input First line of inpu