Bearland big square plane it contain point coordinate exceed 106 absolute valueThere n house Bearland the ith locate point xiyi the n point distinct subset collinearBear Limak live house he want destroy house build new BearlandBears do not like big change for point house pi pj pk sign cross product pjpipkpi relocation if negativepositivezero negativepositivezero respectively this condition satisfy triple index ijk possibly equal different 1 additionally Limak is not allow build house point house exist point old house wasin formula define difference cross product point axay bxby axaybxbyaxbxayby axaybxbyaxbyaybxconsider set possible new placement Limaks house your task find area set pointsformally let Limak choose new placement randomly coordinate choose independently uniformly random interval 106106 let p denote probability getting allow placement new house Let S denote area Bearland S41012 your task find pS