You have a set $S$ that stores distinct points.

Let the points consisted in a walk with $30$ teleportations be
$(x_0,y_0), (x_1,y_1), .., (x_{30},y_{30})$
$(x_0,y_0) = (0,0)$
$(x_{30},y_{30}) = (X,Y)$

For $1 \le i \le 30$
$(x_i,y_i) = (x_{i-1} , y_{i-1} + 2^{i-1})$
or
$(x_i,y_i) = (x_{i-1} + 2^{i-1} , y_{i-1})$

A walk is called a valid walk when $Y$ lies in the range $[123456789,987654321]$.

In a valid walk for $0 \le i \le 29$, insert point $(X - x_i, Y - y_i)$ in set S.

Find the maximum size of set $S$ by taking $28$ valid walks.