Lake Navigation – 2#228
Scientists at a remote research station need to navigate their boat to a measurement buoy located at the center of the lake, at the point with coordinates .
Due to the lake's unusual magnetic properties, boats move according to a peculiar rule. From the point (X_k, Y_k), the boat can move only to the point with coordinates:
where U_k is the control force used to adjust the boat's trajectory. The boat can only be at points with integer coordinates (X_k, Y_k are integers for any k \geq 0). For any k \geq 0, U_k can be any value from the set \{-2, -1, 0, 1, 2\}.
Naturally, the scientists want to reach the buoy as quickly as possible to collect the measurement data. Your task is to determine the minimal possible value for which X_T = 0, Y_T = 0, given the initial position of the boat X_0, Y_0.
The input consists of several tests. Each test is a line with two integers separated by a space — the initial coordinates of the boat X_0, Y_0, where -100 \leq X_0 \leq 100, -100 \leq Y_0 \leq 100. It is guaranteed that it is possible to reach the point from any starting position provided in the input file.
For each initial position X_0, Y_0 in the input, print a single number on a separate line — the minimal possible value for which X_T = 0, Y_T = 0.
Example 1