How to convert list to cycles?

My code below returns the list: {1, 3, 2, 4}. I want the disjoint cycle representation of this permutation. In other words, I want: Cycles[{{2, 3}}]. I tried PermutationCycles[list], but this does not work.

T = {{0, 1}, {1, 0}};
list = Map[MatrixForm, Map[Mod[T.#, 2] &, Tuples[{0, 1}, 2]] /. Table[Tuples[{0, 1}, 2][[i]] -> i, {i, 1, 4}]