You are given an array points, where each element points[i] $= [x_i, y_i, z_i]$ represents a point in three dimensional space, and an array target representing a target point.

At generation $0$, the set of available points consists of all coordinates in points.

In each subsequent generation $k \geq 1$, a new point can be produced from any pair of distinct points $p_1 = [x_1, y_1, z_1]$ and $p_2 = [x_2, y_2, z_2]$ currently present in the set of available points. The coordinates of the new point are given by:

$p_{new} = \left[\left\lfloor \frac{x_1 + x_2}{2} \right\rfloor, \left\lfloor \frac{y_1 + y_2}{2} \right\rfloor, \left\lfloor \frac{z_1 + z_2}{2} \right\rfloor\right]$

Return the minimum generation $k$ at which target becomes available. If target can never be produced, return -1.

Constraints:

• $1 <=$ points.length $<= 20$

• points[i].length $== 3$

• 0 <= points[i][j] $<= 6$

• target.length $== 3$

• 0 <= target[i] $<= 6$

• All points[i] are distinct.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.