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sub fys {
    my $arr = shift;
...
        --$i;
    }
}

@nums = map [ @{$_}[@cols] ], @nums;

my @cols = 0..11;
do {
  fys( \@cols );
} until is_deranged( \@cols );

sub is_deranged {
  my $arr = shift;
  $arr->[ $_ ] == $_ and return for 0..$#$arr;
  return 1;
}

use strict;
use warnings;
...
        @$arr[$i,$j] = @$arr[$j,$i];
    }
}