In chess, each move of a knight consists of moving by two squares horizontally and one square vertically, or by one square horizontally and two squares vertically. A knight making one move from location $(0,0)$ of an infinite chess board would end up at one of the following eight locations: $(1,2)$, $(-1,2)$, $(1,-2)$, $(-1,-2)$, $(2,1)$, $(-2,1)$, $(2,-1)$, $(-2,-1)$.
Starting from location $(0,0)$, what is the minimum number of moves required for a knight to get to some other arbitrary location $(x,y)$?
Each line of input contains two integers $x$ and $y$, each with absolute value at most one billion. The integers designate a location $(x,y)$ on the infinite chess board. The final line contains the word END.
For each location in the input, output a line containing one integer, the minimum number of moves required for a knight to move from $(0,0)$ to $(x, y)$.
|Sample Input 1||Sample Output 1|
1 2 2 4 END