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 $(X_C,Y_C)$.

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

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

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

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

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.