Time Limit: 1 s
Memory Limit: 128 MB

Submission：3
AC：3
Score：99.87

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*).

input

1 2
2 4
END

output

1
2