testt

Start

2022-01-11 20:20 AKST

testt

End

2022-01-11 22:00 AKST
The end is near!
Contest is over.
Not yet started.
Contest is starting in -134 days 12:45:00

1:40:00

0:00:00

Problem EConnect

When constructing electric circuits one has to connect pairs of points using wire, preferable as short as possible. In this problem we have an empty circuit board of size $N \times M$ where we want to connect the two points $A_1$ and $A_2$ with each other using one wire, and the two points $B_1$ and $B_2$ with each other using another wire. The wires must go along the horizontal and vertical edges of the grid (see figure), and the two wires may not share a common vertex. Determine the minimum length of wire needed to do so. The wire may not go outside the circuit board.

Input

The first line contains two integers, $N$ ($2 \le N \le 100$) and $M$ ($2 \le M \le 100$), the grid size of the circuit board.

Then follows four lines containing the coordinates for the points $A_1$, $A_2$, $B_1$ and $B_2$, respectively. Each coordinate pair will be described using two integers and will correspond to an intersection point in the grid. The first coordinate will be between $0$ and $N$ inclusive and the second coordinate between $0$ and $M$ inclusive. All coordinate pairs will be unique.

Output

A single line containing the minimum length of wire needed to connect the points, or “IMPOSSIBLE” if it’s not possible to do so.

Sample Input 1 Sample Output 1
6 3
2 3
4 0
0 2
6 1

IMPOSSIBLE

Sample Input 2 Sample Output 2
6 6
2 1
5 4
4 0
4 5

15