you want party complete laser light show. unfortunately, working laser have found located far away house , heavy move, want re-direct laser light house using series of mirrors. the layout of grid has laser @ position (0,0) pointing north (in positive y direction), , house @ (hx, hy); can think of both laser , house points in 2d plane. there n mirrors (1 <= n <= 100,000) scattered throughout grids aligned @ angles of 45 degrees axes. example, mirror aligned \ take beam of light entering below , reflect left. can think of mirrors being located @ points in 2d plane. after setting configuration, notice major flaw in plan: laser cannot hit house mirrors in current configuration! result, plan run out onto field, , hold 1 more mirror (placed once again @ 45 degree angle) in order redirect laser onto house. please count number of locations in field can stand accomplish goal. all coordinates integers between -1,000,000,000 , 1,000,000,000. guaranteed mirrors placed in range...