# Concave Quadrilaterals

**Computer Science**Level 4

Find \(N+6.\)

**Details and Assumptions:**

As an explicit example, suppose the list had \(2\) lines, and the following numbers were written on those two lines: \[\begin{array}{lrrrrrrrrl} &1, &1, &2, &2, &3, &3, &4, &4 \\ &1, &-1, &2, &-2, &3, &-3, &4, &-4 &.\end{array} \] We have two quadrilaterals, the first one having its vertices at points \((1, 1), (2, 2), (3, 3), (4, 4),\) and the second one having its vertices at points \((1, -1), (2, -2), (3, -3), (4, -4).\) Your job is to find out how many of them are concave.

Link to the file: http://pastebin.ca/2679837.

If one of the vertices lies on the line joining two other vertices, consider the resulting figure as convex.

This is a computer science problem, and is inspired from ProjectEuler (I don't remember the problem number at the moment).