import math


def inradius(a, b, c):
    s = (a + b + c) / 2
    area = (s * (s - a) * (s - b) * (s - c))
    inradius = area / s**2
    return inradius


def euler_195():
    count = 0
    limit = 1053779
    limit2 = limit * limit
    for m in range(0, limit2):
        for n in range(1, m // 2 + 1):
            if math.gcd(m, n) == 1:
                # Generator function from wiki for 60 degree eisenstein
                # triangles.
                a = m**2 - m*n + n**2
                b = 2*m*n - n**2
                c = m**2 - n**2
                gcd = math.gcd(a, b, c)
                a, b, c = a // gcd, b // gcd, c // gcd

                # if gcd == 3 and inradius(a, b, c) > limit2:
                #     break
                if inradius(a / 3, b / 3, c / 3) > limit2:
                    if n == 1:
                        return count
                    break

                if a == b and b == c:
                    continue

                k = 1
                while True:
                    ir = inradius(a*k, b*k, c*k)
                    if ir > limit2:
                        break
                    count += 1
                    k += 1

    return count


if __name__ == "__main__":
    solution = euler_195()
    print("e195.py: " + str(solution))
    assert solution == 75085391