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    \$\begingroup\$ Great second answer! Would you mind sharing the program you used to find the magic numbers? \$\endgroup\$ Commented Jul 12, 2018 at 20:16
  • \$\begingroup\$ Thanks! I just added code to find the magic numbers to the answer, although it isn't terribly pretty. \$\endgroup\$ Commented Jul 13, 2018 at 15:22