## DMPG '15 B6 - Bad S'mores

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Points: 10 (partial)
Time limit: 1.4s
Memory limit: 32M

Author:
Problem type

It is time to set up camp for the night! Bob has built a nice campfire to help everybody keep warm during the night. Every tent would like to be close to the fire, but there is one small problem — Bob's s'more ingredients were expired and many people got sick eating them. As a result, every tent should be close to the washroom as well.

The campsite can be represented as a Cartesian plane.

• The campfire is located at and can provide warmth to tents of at most distance away from the fire as the crow flies (Euclidean distance).
• The washroom is located at , and can be reached by walking along the paths on the campsite.
• The paths in the campsite form a grid, such that each path can be described as a line in the form of or , where is an integer. There is a path for every integral value of , so in total the number of paths is infinite. A tent should be within walking distance along a path (Manhattan distance), such that the distance to the washroom is less than or equal to . A tent can be set up only on an integer coordinate — such that and are integers — and cannot occupy the same position as the fire or washroom.

Can you help Bob determine the maximum amount of tents that can be set up?

#### Input Specification

The first line will contain three integers, , , and . The second line will contain another three integers, , , and . and .
For at least of the marks, and .

#### Output Specification

One integer, the maximum number of tents that can be set up so that it is within range of the fire and the washroom.

#### Sample Input

2 2 2
5 2 3

#### Sample Output

4

#### Diagram for Sample Input

The red circle represents the area the campfire covers, and the blue lines represent the area the washroom covers. Each green dot is a possible location to set up a tent.