Coin Exchange

by Peter Grabarchuk

Take six coins of the same size and arrange them in the capital L altering their heads and tails as shown in the illustration - left position.

The goal is to make another L with all the coins having their heads and tails exchanged as shown in the right position of the illustration. It should be performed in the fewest possible number of moves.

A move consists of sliding a pair of the two adjoining coins to a new place. You have to slide the coins only orthogonally; it means that you are not allowed to rotate the pair of coins while you move it. The final L not necessarily has to be formed exactly at the same spot as the start L was.