Knight's Trip

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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 $(x,y)$?

Input

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.

Output

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
1
2