from collections import Counter
from math import gcd, prod, isqrt
import random

def brent(n):
    y, c, m = random.randint(1, n - 1), random.randint(1, n - 1), random.randint(1, n - 1)
    g, r, q = 1, 1, 1
    while g == 1:
        x = y
        for i in range(r): y = (y * y + c) % n
        k = 0
        while k < r and g == 1:
            ys = y
            for i in range(min(m, r - k)): y, q = (y * y + c) % n, (q * abs(x - y)) % n
            g, k = gcd(q, n), k + m
        r *= 2
    if g == n:
        while True:
            ys, g = (ys * ys + c) % n, gcd(abs(x - ys), n)
            if g > 1: break
    return g

def factors(n):
    c = Counter()
    while n % 2 == 0: c[2], n = c[2] + 1, n // 2
    for p in range(3, 100001, 2):
        while n % p == 0: c[p], n = c[p] + 1, n // p
    while n > 1:
        p = brent(n)
        while n % p == 0: c[p], n = c[p] + 1, n // p
    if n > 1: c[n] += 1
    return c

print(factors(16546864687987117))