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