Four, on a plane there are $n(n \geqslant 4)$ lines. For lines $a$ and $b$, among the remaining $n-2$ lines, if at least two lines intersect with both lines $a$ and $b$, then lines $a$ and $b$ are called a "congruent line pair"; otherwise, they are called a "separated line pair". If the number of congruent line pairs among the $n$ lines is 2012 more than the number of separated line pairs, find the minimum possible value of $n$ (the order of the lines in a pair does not matter).
(1) Among these $n$ lines, if there exist four lines that are pairwise non-parallel, then any two lines are coincident line pairs. However, $\mathrm{C}_{n}^{2}=2012$ has no integer solution, so there does not exist an $n$ that satisfies the condition.
(2) If the $n$ lines have only three different directions, let the number of lines in these three directions be $a$, $b$, and $c$ respectively. Assume $a \geqslant b \geqslant c$.
(i) When $a \geqslant 2, b=c=1$,
$$
\mathrm{C}_{a}^{2}+1-2 a=2012,
$$

there is no $n$ that satisfies the condition.
(ii) When $a, b \geqslant 2, c=1$,
$$
\mathrm{C}_{a}^{2}+\mathrm{C}_{b}^{2}-a b+b+a=2012,
$$

which simplifies to $(a-b)^{2}+a+b=4024$.
Let $a-b=k$. Then $a+b=4024-k^{2}$.
Thus, $a=\frac{4024+k-k^{2}}{2}, b=\frac{4024-k-k^{2}}{2}$.
Since $b \geqslant 2$, it is easy to see that $k \leqslant 62$.
Therefore, the minimum value of $a+b$ is 180.
Thus, the minimum value of $n$ is 181.
(iii) When $a, b, c \geqslant 2$,
$$
\mathrm{C}_{a}^{2}+\mathrm{C}_{b}^{2}+\mathrm{C}_{c}^{2}+a b+b c+c a=2012,
$$

which simplifies to $(a+b+c)(a+b+c-1)=4024$,
and there is no integer solution.
(3) If the $n$ lines have only two different directions, let the number of lines in these two directions be $a$ and $b$ respectively. Clearly, $a, b \geqslant 2$.
Then $\mathrm{C}_{a}^{2}+\mathrm{C}_{b}^{2}-a b=2012$, which simplifies to
$$
(a-b)^{2}-(a+b)=4024.
$$

Let $a-b=k$. Then $a+b=k^{2}-4024$.
Thus, $a=\frac{k+k^{2}-4024}{2}, b=\frac{k^{2}-k-4024}{2}$.
Since $b \geqslant 2$, it is easy to see that $k \geqslant 64$.
Therefore, the minimum value of $a+b$ is 72.
Thus, the minimum value of $n$ is 72.
In summary, the minimum value of $n$ is 72.