import math

max_l = 0
def check(coeffs, K, l):
    if K == 0:
        global max_l
        max_l = max(max_l, l)
        for i in range(1, min(3, l)+1):
            # l - i + 1 terms
            c = sum(coeffs[-j][0]*coeffs[-(l-i+2-j)][1] for j in range(1, l-i+2))
            if c != 0:
                return

        print(coeffs)
        return
    B = sum(coeffs[i][0]*coeffs[-i][1] for i in range(1, l+1))
    M = math.isqrt(K)
    for bl1 in range(-M, M+1):
        if (B - bl1) % 3 == 0:
            bnl1 = (B - bl1) // 3
            K_next = K - bl1*bl1 - bnl1*bnl1
            if K_next >= 0:
                check([*coeffs, (bl1, bnl1)], K_next, l+1)


check([(3, 1), (5, 0)], 0, 1)
check([(3, 1), (-4, 3)], 0, 1)
check([(3, 1), (2, 1)], 20, 1)
check([(3, 1), (-1, 2)], 20, 1)

print(f"max l = {max_l}")