Packing Rectangles

Figure 1: The six basic layouts of four rectangles

You are given four rectangles. Find the smallest enclosing rectangle into which all four fit without overlapping. "Smallest" means the one with the least area.

Every rectangle must have its sides parallel to the corresponding sides of the enclosing rectangle. Figure 1 shows the six ways to fit four rectangles together; every other arrangement can be obtained from one of these basic layouts by rotation or reflection, so these six are the only basic layouts.

Each rectangle may be placed in either orientation (rotated by $90°$). Several different enclosing rectangles with the same minimum area may exist, and you must report all of them.

The input consists of four lines. Each line describes one rectangle by two positive integers: the lengths of its two sides. Each side length is between $1$ and $50$, inclusive.

Print one line more than the number of solutions. The first line contains a single integer: the minimum area of an enclosing rectangle. Each of the following lines describes one solution by two numbers $p$ and $q$ with $p \le q$. These lines must be sorted in ascending order of $p$ and must all be distinct.