Connection

When you connect two points with a wire in an electric circuit, a shorter wire is better.

Four points $A_1$, $A_2$, $B_1$, and $B_2$ are given on an empty $N \times M$ circuit board. You want to connect $A_1$ to $A_2$ with one wire and $B_1$ to $B_2$ with another wire.

The board is a grid, and each lattice point has coordinates $(x, y)$ with $0 \le x \le N$ and $0 \le y \le M$. A wire may run only along the unit vertical or horizontal segments of the grid, and it may never leave the board.

The two wires must not touch each other: they may not share any lattice point and may not cross. (It is fine for the two wires to run side by side one cell apart.)

Write a program that finds the minimum possible total length of the two wires.

The first line contains the board dimensions $N$ and $M$, separated by a space. ($2 \le N, M \le 100$)

Each of the next four lines contains the coordinates of $A_1$, $A_2$, $B_1$, and $B_2$, in that order. Each coordinate consists of two integers $x$ and $y$ with $0 \le x \le N$ and $0 \le y \le M$. All four points are at distinct positions.

Print the minimum possible total length of the two wires connecting $A_1$-$A_2$ and $B_1$-$B_2$. If it is impossible to place the two wires under the given conditions, print IMPOSSIBLE.