Let A, B.C, D be (not necessarily) real matrices such that ${\mathrm{A}}^{\mathrm{T}}=\mathrm{BCD};{\mathrm{B}}^{\mathrm{T}}=\mathrm{CDA};{\mathrm{C}}^{\mathrm{T}}=\mathrm{DAB}\text{ and }{\mathrm{D}}^{\mathrm{T}}=\mathrm{ABC}$ for the matrix S = ABCD, the least value of k such that S^k = S is