sub index_by_length {
    my $conn_a = $Connections[$a];
    my $diff_a = $conn_a->[0] - $conn_a->[1];
    my $conn_b = $Connections[$b];
    my $diff_b = $conn_b->[0] - $conn_b->[1];
    return $diff_a*$diff_a <=> $diff_b*$diff_b;
}

my @sorted_indices = sort index_by_length 0..$#Connections;