Practice Permutations and Combinations with the exercise "Kids Blocks"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Permutations

Statement

Goal

Given a set of KIDS BLOCKS,

The blocks pieces can be categorized into exactly THREE SUBSETS based on their widths:
- One inch pieces.
- Two inches pieces.
- and Three inches pieces.
All have the same height (One inch).

The problem is to determine if it is feasible to build a perfect rectangular wall (or square), with below conditions:
- Must use all pieces.
- The wall height must be two inches or more (two rows of blocks pieces at minimum).

Note 1: If all available pieces were of the same size, It is considered a correct solution to stack them vertically, But not a solution to just queue them horizontally.

The program takes three integers as inputs which are:
x1 , x2, and x3 --> the count of pieces in each subset respectively.

The program should print either "POSSIBLE" or "NOT POSSIBLE" to indicate if a rectangular wall is buildable based on above rules.

Note 2: The given set of pieces might produce several solutions (different possible walls with different dimensions), so you can simply consider the wall is buildable once ANY solution found.

Example:
Pieces:

 5 × [_"_]
 2 × [_"____"_]
 1 × [_"____"____"_]

Examples of wall:
6×2

[_"_][_"_][_"____"____"_][_"_]
[_"____"_][_"_][_"____"_][_"_]

3×4

[_"_][_"_][_"_]
[_"_][_"____"_]
[_"____"_][_"_]
[_"____"____"_]

Input

Line 1: An integer x1 for the count of one-inch pieces (can be zero).
Line 2: An integer x2 for the count of two-inches pieces (can be zero).
Line 3: An integer x3 for the count of three-inches pieces (can be zero).

Output

A single line contains one string "POSSIBLE" or "NOT POSSIBLE".

Constraints

0 ≤ x1, x2, x3 ≤ 30
- The wall should make use of all these pieces.
- The wall should consist of two rows or more (not a solution to just queue all pieces in one row!)

Example

Input

1
1
1

Output

POSSIBLE

Solve it

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