Connect

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.

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.

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 |
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6 6 2 1 5 4 4 0 4 5 |
15 |