We are given $$$n$$$ points $$$(x_i, y_i)$$$, each with a transmission radius $$$r_i$$$. If a point already has the signal, it will transmit the signal to another point if:

or

Once a point receives the signal, it will also start transmitting according to the same rule.

Task: Find the minimum number of points that must be directly connected to the signal so that, starting from these initially connected points, all $$$n$$$ points will eventually receive the signal. Example:

3

1 0 1

2 0 1

5 0 1

Output:

2