Problem Statement

There is an infinite two-dimensional grid, and we have a piece called Super Ryuma at square $(r_1, c_1)$. (Ryu means dragon and Ma means horse.) In one move, the piece can go to one of the squares shown below:

More formally, when Super Ryuma is at square $(a, b)$, it can go to square $(c, d)$ such that at least one of the following holds:

• $a + b = c + d$
• $a - b = c - d$
• $|a - c| + |b - d| \le 3$

Find the minimum number of moves needed for the piece to reach $(r_2, c_2)$ from $(r_1, c_1)$.

Constraints

• All values in input are integers.
• $1 \le r_1, c_1, r_2, c_2 \le 10^9$

Input

Input is given from Standard Input in the following format:

r_1 c_1
r_2 c_2

Output

Print the minimum number of moves needed for Super Ryuma to reach $(r_2, c_2)$ from $(r_1, c_1)$.