If  $x_1,x_2,x_3\mathrm{..........}{x}_n$ are sequence of integers such that $-1\le x_i\le 2$  and  $x_1+x_2+x_3+\mathrm{.......}+x_n=19$, $x_1^2+x_2^2+x_3^2+\mathrm{.......}+x_n^2=99$  then $\frac{maximumvalueof(x_1^3+x_2^3+\mathrm{.......}+x_n^3)}{minimumvalueof(x_1^3+x_2^3+\mathrm{.......}+x_n^3)}$   is _______

-1, 1, 2 are integers to be used for  
$\begin{array}{l}\text{Suppose }(-1)usedx-times\\ 1usedy-times\\ 2usedz-times\end{array}\}then\begin{array}{c}x(-1)+y\left(1\right)+z\left(2\right)=19\to \left(1\right)\\ x{(-1)}^2+y{\left(1\right)}^2+z{\left(2\right)}^2=99\to \left(2\right)\end{array}$
On solving  $x+z=40$
$2y+6z=118$
$y=59-3z\ge 0$
$z\le 19.2$
Let us find out min and max value of  $x{(-1)}^3+y{\left(1\right)}^3+z{\left(2\right)}^3$
 $=-x+y+8z$
  $=z-40+59-3z+8z$
  $=6z+19\to \min \to 19$
    $\max \to 19\left(7\right)$