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Triangle Classification

Classify three side lengths as invalid, equilateral, isosceles, or scalene.

Problem

Classify three side lengths as invalid, equilateral, isosceles, or scalene. A valid triangle has positive sides, and its two shortest sides must sum to more than its longest side. Equal-to is invalid: it forms a straight line. Use equilateral for three equal sides, isosceles for exactly two, and scalene for three different sides.

Implement triangle_classification(sides).

Input

sides: The three side lengths in any order.

Output

Return one lowercase label: invalid, equilateral, isosceles, or scalene.

Constraints

Exactly three integer sides, each between −1,000,000,000 and 1,000,000,000. Nonpositive sides are invalid.

Examples

Example 1
Input:
sides = [5, 5, 8]

Expected output:
expected = "isosceles"
Input:
std::vector<long long> sides = {5, 5, 8};

Expected output:
std::string expected = "isosceles";
Input:
long[] sides = new long[] {5, 5, 8};

Expected output:
string expected = "isosceles";

Explanation

Two sides equal 5, and 5 + 5 > 8, so this is a valid isosceles triangle.

Example 2
Input:
sides = [1, 2, 3]

Expected output:
expected = "invalid"
Input:
std::vector<long long> sides = {1, 2, 3};

Expected output:
std::string expected = "invalid";
Input:
long[] sides = new long[] {1, 2, 3};

Expected output:
string expected = "invalid";

Explanation

1 + 2 equals 3. The strict inequality fails, so these lengths form a line.

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

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