next if $i == $j;
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This line is unnecessary. It's been discussed before here and elsewhere, but in an array of any significant size (>10 or 20 or so), the odds that i and j are equal are low enough that the logic to test if they are equal outweighs the cost of just swapping the array element with itself (i.e. you're testing to see if they're equal on every iteration, costing something on every iteration, where if you dont' test you'd hardly ever be swapping something with itself anyway).