Problem 44776. Lights Out 15 - 5x5, broken buttons I

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.

This problem contains 5x5 boards that require any number of moves to solve. However, the game has a glitch now—each time you press a button, it doesn't toggle itself, only those lights that are adjacent. That is to say, all buttons toggle two, three, or four lights (indices), rather than the normal three, four, or five, respectively.

For example, if:

 board = [0 1 0 0 0  
          1 0 0 1 0  
          0 0 1 0 1  
          0 1 0 1 0  
          1 0 1 0 0]

the answer is:

 moves = [1 10 18]

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