Coins in motion

Three A coins, three B coins and three C coins are online in the ABCABCABC order as shown in the drawing. You have to move them until they are in the AAABBBCCC order.

Rules:

  • A movement is to support the index finger and the big toe on two coins that touch, and to move them to another place on the line.

  • During the move, the pair of coins can not be swapped, and after the move the pair must be touching some other coin of the line.

  • It may happen that some coins are isolated as a result of a play, but no pair can be taken to a position totally isolated from the rest.

  • It is not required that in the end all the coins are forming a compact line; there may be gaps.

Is it possible to do the rearrangement in four moves?

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