End of the Line-b

There are some boxes in a line, each marked with a letter from A–Z. You would like to reorder the boxes so that boxes marked with the same letter appear next to each other in the line (though they do not have to be in alphabetical order). You can take a box from anywhere in the line, and put it on the rightmost end.

For example, take the following line: \(\text{A C B A D C B B}%speech% . A, C, B, A, D, C, B, B\).

One way to get them into a correct order is to move the leftmost B and then the two Cs.

\( \text{A C B A D C B B} \xrightarrow{\text{left B}} \text{A C A D C B B B} \xrightarrow{\text{right C}} \text{A C A D B B B C} \xrightarrow{\text{left C}} \text{A A D B B B C C}\)

This takes three moves and is the fewest possible to order the boxes.


For the line of boxes below, what is the fewest number of moves you need to reorder the boxes?

\(\text{A B B C D C A E F D F G G E X X X X X X X X X X}\)