'''
Define prime factors of integer m.
Return a list of pairs: (prime divisor, its exponent)
For example:
factorize(100)
[(2, 2), (5, 2)]
foctorize(1024)
[(2, 10)]
'''
def factorize(m):
    res = []
    d = 2
    while d*d <= m:
        e = 0
        while m%d == 0:
            m //= d
            e += 1
        if e > 0:
            res.append((d, e))
        d += 1
    if m != 1:
        res.append((m, 1))
    return res
    
def main():
    print("Factorization of integers")
    while True:
        s = input("n: ")
        try:
            n = int(s)
        except ValueError:
            break
        res = factorize(n)
        print(res)
        
if __name__ == "__main__":
    main()