sub rotate_matrix {
    my ($matrix, $r) = @_;
    my $rows = scalar @$matrix;
    my $cols = scalar @{$matrix->[0]};
    
    my $num_layers = int(min($rows, $cols) / 2);
    
    for my $layer (0 .. $num_layers - 1) {
        my @ring = extract_ring($matrix, $layer, $rows, $cols);
        my $perimeter = scalar @ring;

        my $effective_r = $r % $perimeter;
        @ring = (@ring[$effective_r .. $#ring], @ring[0 .. $effective_r - 1]);
        
        place_ring($matrix, \@ring, $layer, $rows, $cols);
    }
}

sub extract_ring {
    my ($matrix, $layer, $rows, $cols) = @_;
    my @ring;

    for my $i ($layer .. $cols - $layer - 1) {
        push @ring, $matrix->[$layer][$i];
    }

    for my $i ($layer + 1 .. $rows - $layer - 1) {
        push @ring, $matrix->[$i][$cols - $layer - 1];
    }

    for my $i (reverse $layer .. $cols - $layer - 2) {
        push @ring, $matrix->[$rows - $layer - 1][$i];
    }

    for my $i (reverse $layer + 1 .. $rows - $layer - 2) {
        push @ring, $matrix->[$i][$layer];
    }

    return @ring;
}

sub place_ring {
    my ($matrix, $ring_ref, $layer, $rows, $cols) = @_;
    my @ring = @$ring_ref;
    my $index = 0;

    for my $i ($layer .. $cols - $layer - 1) {
        $matrix->[$layer][$i] = $ring[$index++];
    }

    for my $i ($layer + 1 .. $rows - $layer - 1) {
        $matrix->[$i][$cols - $layer - 1] = $ring[$index++];
    }

    for my $i (reverse $layer .. $cols - $layer - 2) {
        $matrix->[$rows - $layer - 1][$i] = $ring[$index++];
    }

    for my $i (reverse $layer + 1 .. $rows - $layer - 2) {
        $matrix->[$i][$layer] = $ring[$index++];
    }
}

sub matrixRotation {
    my ($matrix, $r) = @_;
    
    rotate_matrix($matrix, $r);    
    foreach my $row (@$matrix) {
        print "@$row\n";
    }
}

sub min {
    return $_[0] < $_[1] ? $_[0] : $_[1];
}