Find Right-Triangle Triples

Find every triple of positive integers a < b < c for which a² + b² = c² and a + b + c = perimeter. Return each triple as [a, b, c], ordered by increasing a and then b. Do not include permutations of the same sides.

Implement pythagorean_triplets(perimeter).

Input

perimeter: The required sum of all three sides.

Output

Return a list of triples in the specified order.

Vincoli

3 ≤ perimeter ≤ 100,000. Return an empty list if no triangle qualifies.

Esempi

Input:
perimeter = 30

Output atteso:
expected = [
    [5, 12, 13]
]

Input:
long long perimeter = 30;

Output atteso:
std::vector<std::vector<long long>> expected = {
    {5, 12, 13}
};

Input:
long perimeter = 30;

Output atteso:
long[][] expected = new long[][] {
    new long[] {5, 12, 13}
};

Input:
perimeter = 11

Output atteso:
expected = []

Input:
long long perimeter = 11;

Output atteso:
std::vector<std::vector<long long>> expected = {};

Input:
long perimeter = 11;

Output atteso:
long[][] expected = new long[][] {};

Riferimenti

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• Pythagorean Triplet