The points S(i,j) with integer Cartesian coordinates 0<i≤n,0<j≤m,m≤n, form a lattice. Find the number of:(a) rectangles with vertices on the lattice and sides parallel to the coordinate axes;(b) squares with vertices on the lattice and sides parallel to the coordinate axes;(c) squares in total, with vertices on the lattice. geometryrectangleanalytic geometryvectorcombinatorics proposedcombinatorics