def isPrime(m):
    if m in [2, 3, 5, 7, 11, 13, 17, 19]:
        return True
    if m < 20 or m%2 == 0:
        return False
    d = 3
    while d*d <= m:
        if m%d == 0:
            return False
        d += 2
    return True
    
def factorize(m):
    if m == 0:
        return []
    res = []
    if m < 0:
        res.append((-1, 1))
        m = (-m)
    assert m > 0
    d = 2
    while d*d <= m:
        if m%d == 0:
            e = 1
            m //= d
            while m%d == 0:
                e += 1
                m //= d
            res.append((d, e))     
        d += 1
    if m > 1:
        res.append((m, 1))
    return res    

def dividers(m):
    return [ d for d in range(1, m//2 + 1) if m%d == 0 ] 
    
def isPerfect(m):
    return sum(dividers(m)) == m