Label the vertices of a square 1, 2, 3, 4 in counterclockwise order, with 1 being at the top right. The group D4 acts on the vertices as permutations [e.g., r acts as (1234) and s acts as (24)] and thus also D4 acts as permutations on pairs of vertices: r([1, 2]) = [2, 3], r([1, 3]) = [2, 4], and so on. There are six pairs of vertices: P = {[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]}.

Find the disjoint cycle decomposition of r and s as permutations of the six elements of P.