Knight's Marathon

The invading army is beaten at last. The king sends his only surviving knight to the capital to tell the people about the victory. The trip may be a very long one.

The knight moves the way a knight moves on a chessboard. In one move he travels two squares in one of the four compass directions, then one more square at a right angle to that direction. He must stay inside the kingdom for the whole trip so that he does not start a new war. The kingdom is a rectangular grid of size $NX \times NY$, possibly much larger than the $8 \times 8$ board the battle was fought on. Rows and columns are numbered from 0. The knight starts at square $(KX, KY)$ and must reach the capital at square $(CX, CY)$. Find the smallest number of moves in which the knight can reach the capital.

Figure 1: the squares a knight can reach in one move.

The input has three lines, each with two integers.

• The first line has the size of the kingdom, $NX$ and $NY$ ($8 \le NX, NY \le 10^9$).
• The second line has the starting position of the knight, $KX$ and $KY$ ($0 \le KX < NX$, $0 \le KY < NY$).
• The third line has the position of the capital, $CX$ and $CY$ ($0 \le CX < NX$, $0 \le CY < NY$).

Print one line with the smallest number of moves the knight needs to reach the capital.