N-orthotope

An axis parallel N-orthotope is the set of N dimensional points written in this form.

$[s_1, e_1] \times [s_2, e_2] \times \cdots \times [s_N, e_N] \quad (s_i < e_i)$

That is, it collects every point $(x_1, x_2, \ldots, x_N)$ whose coordinate $x_i$ satisfies $s_i \le x_i \le e_i$.

• For $N = 0$ the set is defined as a point in 0 dimensions.
• For $N = 1$ it is a segment on a line.
• For $N = 2$ it is an axis parallel rectangular region in the plane.
• For $N = 3$ it is an axis parallel rectangular box in space.

Generalize a little and allow $s_i \le e_i$ in the product

$[s_1, e_1] \times [s_2, e_2] \times \cdots \times [s_K, e_K] \quad (s_i \le e_i)$

If exactly $N$ indices satisfy $s_i < e_i$, this set of points is an axis parallel N-orthotope. The words 'axis parallel' are dropped from here on, but every orthotope below is still axis parallel.

Two N-orthotopes are given for some $N$. If some points belong to both regions at once, those points form an M-orthotope. Write a program that computes $M$. For 2-orthotopes there are the four cases below.

• In A the common region is again a 2-orthotope.
• In B the common region is a 1-orthotope, a segment.
• In C the common region is a 0-orthotope, a point.
• In D there is no common region. Print -1 in that case.

The first line has a natural number $N$.

The second line has $s_1, e_1, s_2, e_2, \ldots, s_N, e_N$ of the first region, separated by spaces.

The third line has $s_1, e_1, s_2, e_2, \ldots, s_N, e_N$ of the second region, separated by spaces.

Every given number is an integer with absolute value at most 11, and $s_i < e_i$ holds for each $i$.

$1 \le N \le 11$.

On the first line print $M$ if the common region of the two regions is an M-orthotope. If there is no common region, print -1.