Call a sequence $1<X_1\le \cdots X_m\le n$ line-compatible if there is a set of $n$ points in ${\mathbb{R}}^2$ such that there are $m$ lines ${\ell }_1,\dots ,{\ell }_m$ containing at least two points, and the number of points on ${\ell }_i$ is exactly $X_i$.Prove that there are at most$$\exp (O(n^{1/2}))$$many line-compatible sequences.