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## triangle1 – Three Triangle Types (challenge)

Every triangle can be classified as either scalene, isosceles or equilateral:

*equilateral* triangles have all edges of the same size;
*isosceles* triangles have exactly two edges of the same size;
*scalene* triangles have three edges of different sizes.

(Some authors consider equilateral to be a special case of isosceles. For the
purpose of this exercise, we use Euclid’s original definition and consider
isosceles triangles those with *exactly* two edges of the same size.)

Write a program that given three edge sizes determines whether a triangle is
*scalene*,
*isosceles*,
*equilateral*
or *impossible*.

### Input and Output

The input consists of a single line with three natural numbers *x*, *y* and *z*
where
0 < x, y, z < 100

The output should contain a single line with just
`scalene`

,
`isosceles`

,
`equilateral`

or `impossible`

.

#### Example input 1

```
3 4 5
```

#### Example output 1

```
scalene
```

#### Example input 2

```
3 3 1
```

#### Example output 2

```
isosceles
```

#### Example input 3

```
6 2 3
```

#### Example output 3

```
impossible
```

#### Example input 4

```
4 4 4
```

#### Example output 4

```
equilateral
```

### Scoring

- 4/12: works for the above examples
- 12/12: works for other test cases

### Hints

If are having trouble to get a full score in this exercise,
try to come up with other test cases besides
the ones given on the example inputs.
Does your program still produce the expected results on them?
What if you change the order in which the sides are given?

try first: good1 signum1

try next: factorial1

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