Help reorder the alphabet 3

Line up the $26$ letters in the alphabet randomly in a line. The alphabet letters are not necessarily in sorted order. To bring the letters back into sorted order, you are only allowed to cycle three letters. For example, you can cycle the letters $a,b,c$ by sending $a$ to $b$ , $b$ to $c$ and $c$ to $a$ .

Assuming that the row of letters can be brought back into sorted order with only three-cycles, what is the maximum number of three-cycles you need to bring the letters back to sorted order.