given any 3 distinct points $X,Y,Z$on the integer coordinates of the x-axis,the following operation is allowed:A point say $X$ is reflected over another point say $Y$. Note that after each operation only one among three points is moved. we perform these operations till 2 out of the 3 points coincide. let $N=N(X,Y,Z)$ denote the minimum number of operations before we are forced to stop.(this could happen in different ways). show that there are at most $2^N$coordinates that point $X$ could end up if we are forced to stop after $N$operations