Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x^2-12 x+[x]+31=0$ and $x^2-5 \mid x+ 2 \mid-4=0$ respectively, where $[x]$ denotes the greatest integer $\leq x$. Then $m^2+m n+n^2$ is equal to $\_\_\_\_$ .
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