from tools import number_theory

def make(x, y, z):
    return x ** 2 + y ** 3 + z ** 4

def count(limit):
    result = set()
    prime = list(number_theory.make_prime(int(limit ** 0.5) + 1))
    for i in prime:
        for j in prime:
            for k in prime:
                trns = make(i, j, k)
                if trns > limit:
                    break
                result.add(trns)
            if make(i, j, 2) > limit:
                break
        if make(i, 2, 2) > limit:
            break
    return result

print(len(count(50000000)))