Let $L_1, L_2$ be the lines passing through the point $P(0,1)$ and touching the parabola $9 x^2+12 x+18 y- 14=0$. Let $Q$ and $R$ be the points on the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ such that the $\triangle \mathrm{PQR}$ is an isosceles triangle with base $Q R$. If the slopes of the lines $Q R$ are $m_1$ and $m_2$. then $16\left(\mathrm{~m}_1^2+\mathrm{m}_2^2\right)$ is equal to $\_\_\_\_$ .