The Magical Stone

Initially, there is a magical stone of mass $2^N$ lying at the origin of the number line. For the next $N$ seconds, the following event happens: - Let us define the *decomposition* of a magical stone as follows: If there is a magical stone of mass $M > 1$ lying at coordinate $X$, then it decomposes into two magical stones, each of mass $\frac{M}{2}$ lying at the coordinates $X-1$ and $X+1$ respe