In an infinite chess board with coordinates from -infinity to +infinity, you have a knight at square [0, 0].

A knight has 8 possible moves it can make, as illustrated below. Each move is two squares in a cardinal direction, then one square in an orthogonal direction.

Return the minimum number of steps needed to move the knight to the square [x, y]. It is guaranteed the answer exists.

 

Example 1:

Input: x = 2, y = 1
Output: 1
Explanation: [0, 0] → [2, 1]

Example 2:

Input: x = 5, y = 5
Output: 4
Explanation: [0, 0] → [2, 1] → [4, 2] → [3, 4] → [5, 5]

 

Constraints:

• -300 <= x, y <= 300
• 0 <= |x| + |y| <= 300