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my $n = 20;
my $k = 5;

for (my $t=0;$t<10;$t++)  {

    my @l = map { int(rand($k)) } 1..$n;

    my $best_start = 0;
    my $best_direction = 1;

    for (my $s = 0;$s<$n;$s++) {
	foreach my $d (-1,1) {
	    my $f1 = $s;
	    my $f2 = $best_start;
	    for (my $i=0;$i<$n;$i++) {
		my $c = $l[($f1+$n)%$n] <=> $l[($f2+$n)%$n];
		if ($c!=0) {
		    if ($c<0) {
			$best_start = $s;
			$best_direction = $d;
		    }
		    last;
		}
		$f1 += $d;
		$f2 += $best_direction;
	    }
	}
    }

    my @n = @l[map { ($best_direction*$_+$best_start+$n)%$n } 0..$n-1];

    print "original: @l\n";
    print "normal:   @n\n";
    print "\n";
}