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).

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).

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.

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

见题面 Input 部分

见题面 Output 部分