If R is the least value of $a$ such that the function  $f\left(x\right) = x^2 + ax + 1$ is increasing on [1,2] and S is the greatest value of $a$ such that the function $f\left(x\right) = x^2 + ax + 1$ is decreasing on [1,2] then the value of $\left|\mathrm{R}-\mathrm{S}\right|$ is------