Problem 44769. Lights Out 14 - 5x5, four stages, x moves

Lights Out is a logic game wherein all lights need to be turned off to complete each board. See the first problem in the series for an introduction and problem 12 for an explanation of three stages.

This problem contains boards that each require any number of moves to solve. In addition, lights are now activated through four stages: on1 (1) to on2 (2) to on3 (3) to off (0). For example, if

 board = [1 1 0 0 3  
          1 0 0 3 3  
          0 0 0 0 3  
          0 0 2 0 0  
          0 2 2 2 0]

the answer is:

 moves = [1 1 1 15 15 22]

Up to three moves are possible for each button (index).

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