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sub lower_bound1 {
  my @sorted;
...
  }
  return $min/2;
}

     0    1    2    3    4      min1          min2
0    0    1   (2)   3    1      1                
...

lower_bound2: 19 = sum(min2)/2 - 15 + 1 + 1
   (excluding col 0 and 4 for double rows, striking the maximum)