There are $n$ ($n \ge 4$) straight lines on the plane. For two straight lines $a$ and $b$, if there are at least two straight lines among the remaining $n-2$ lines that intersect both straight lines $a$ and $b$, then $a$ and $b$ are called a congruent pair of staight lines, otherwise it is called a separated pair of straight lines. If the number of congruent pairs of straight line among $n$ straight lines is $2012$ more than the number of separated pairs of straight line , find the smallest possible value of $n$ (the order of the two straight lines in a pair is not counted).