# Replace:
    my @sorted= sort @list;

# with:
    my @index= sort {
        $list[$a] cmp $list[$b] || $a <=> $b
    } 0..$#list;
    my @sorted= @list[@index];

# or with (to avoid @index remaining in scope):
    my @sorted= @list[
        sort {
            $list[$a] cmp $list[$b] || $a <=> $b
        } 0..$#list
    ];