The Cubes#11674
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The Cubes

1 second
256 megabytes
Easy

You are given cubes of blue, yellow, and green colors. There are , , and cubes of each color, respectively. All the cubes of each color are uniquely numbered from to , , and (so all the cubes are distinct).

A set of cubes is called interesting if it contains at least two cubes and all cubes in it have different colors.

Count the number of interesting sets you can construct from the given cubes.

For example, if there is blue cube, yellow cubes, and green cube, there are interesting sets:

  1. first blue cube and first yellow cube;

  2. first blue cube and second yellow cube;

  3. first blue cube and first green cube;

  4. first yellow cube and first green cube;

  5. second yellow cube and first green cube;

  6. first blue cube, first yellow cube and first green cube;

  7. first blue cube, second yellow cube and first green cube;

Input

The only line contains three integers , , (0 \le a, b, c \le 1000) — the number of cubes of each color.

Output

Print the number of interesting sets of cubes.

Examples

Example

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Example 1

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Example 2

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Note

The first test is explained in the statement.

In the second test, there are only interesting sets of cubes:

  1. first yellow cube and first green cube;

  2. second yellow cube and first green cube.

Scoring

  1. ( points): a, b, c \le 1;

  2. ( points): b = 0, c = 0;

  3. ( points): c = 0;

  4. ( points): no additional constraints.