Practice Tiling with the exercise "Kids Blocks"

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).

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 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.

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-inch pieces (can be zero).
Line 3: An integer x3 for the count of three-inch pieces (can be zero).

Output

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

Constraints

0 ≤ x1, x2, x3 ≤ 30

Example

Input

1
1
1

Output

POSSIBLE

Solve it

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