Resolution of a problem of Mohar on non-positive inertia

For a graph $G$ of order $n$, its positive, negative and non-positive inertia is the number of positive, negative and non-positive eigenvalues of its adjacency matrix $A(G)$, respectively. Mohar asked whether every graph with $k$ non-positive eigenvalues has order $O(k^2)$ as $k\to \infty$. Using NE