103235: [Atcoder]ABC323 F - Push and Carry

Problem Statement

Takahashi and a cargo are on a coordinate plane.

Takahashi is currently at $(X_A,Y_A)$, and the cargo is at $(X_B,Y_B)$. He wants to move the cargo to $(X_C,Y_C)$.

When he is at $(x,y)$, he can make one of the following moves in a single action.

• Move to $(x+1,y)$. If the cargo is at $(x+1,y)$ before the move, move it to $(x+2,y)$.
• Move to $(x-1,y)$. If the cargo is at $(x-1,y)$ before the move, move it to $(x-2,y)$.
• Move to $(x,y+1)$. If the cargo is at $(x,y+1)$ before the move, move it to $(x,y+2)$.
• Move to $(x,y-1)$. If the cargo is at $(x,y-1)$ before the move, move it to $(x,y-2)$.

Find the minimum number of actions required to move the cargo to $(X_C,Y_C)$.

Constraints

• $-10^{17}\leq X_A,Y_A,X_B,Y_B,X_C,Y_C\leq 10^{17}$
• $(X_A,Y_A)\neq (X_B,Y_B)$
• $(X_B,Y_B)\neq (X_C,Y_C)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$X_A$ $Y_A$ $X_B$ $Y_B$ $X_C$ $Y_C$

Output

Print the minimum number of actions required to move the cargo to $(X_C,Y_C)$.

Sample Input 1

1 2 3 3 0 5

Sample Output 1

9

Takahashi can move the cargo to $(0,5)$ in nine actions as follows.

• Move to $(2,2)$.
• Move to $(3,2)$.
• Move to $(3,3)$. The cargo moves to $(3,4)$.
• Move to $(3,4)$. The cargo moves to $(3,5)$.
• Move to $(4,4)$.
• Move to $(4,5)$.
• Move to $(3,5)$. The cargo moves to $(2,5)$.
• Move to $(2,5)$. The cargo moves to $(1,5)$.
• Move to $(1,5)$. The cargo moves to $(0,5)$.

It is impossible to move the cargo to $(0,5)$ in eight or fewer actions, so you should print $9$.

Sample Input 2

0 0 1 0 -1 0

Sample Output 2

6

Sample Input 3

-100000000000000000 -100000000000000000 100000000000000000 100000000000000000 -100000000000000000 -100000000000000000

Sample Output 3

800000000000000003