M2S3: From 11 to 25

In the game of M2S3, the goal is to use minimum number of steps to get from one number to the next. In each step, you can either

  • multiply by 2, or
  • subtract 3.

For example, if we wanted to get from 8 to 11, we could do so in 5 steps:

835×21037×214311.\large 8 \overset{-3}{\longrightarrow} 5 \overset{\times2}{\longrightarrow}10 \overset{-3}{\longrightarrow} 7\overset{\times2}{\longrightarrow}14 \overset{-3}{\longrightarrow}11.

What is the minimum possible number of steps required to get from 11 to 25?


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