Buggy python submission (verdict: Time Limit Exceeded):
import math

def isPrime(num):
    if num < 2:
        return False
    elif num == 2:
        return True
    elif num % 2 == 0:
        return False

    for i in range(3, math.floor(math.sqrt(num))+1, 2):
        if num % i == 0:
            return False
    return True


def find_all_prime(num):
    prime_list = [2]
    for i in range(3, num, 2):
        if isPrime(i):
            prime_list.append(i)

    return prime_list


if __name__ == "__main__":
    N = int(input())
    if isPrime(N):
        print(1)
    else:      
        prime_list = find_all_prime(int(1.25*10**6))
        count = 0  
        for i in prime_list:
            j = 1
            while N > 1:
                if N // i**j == 0:
                    break
                if N % i**j == 0:
                    N = N // i**j
                    count += 1
                j +=1
        
        print(count)

Fixed submission:
def factorization(n):
    factorization_list = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp % i == 0:
            count = 0
            while temp % i == 0:
                count += 1
                temp //= i
            factorization_list.append([i, count])

    if temp != 1:
        factorization_list.append([temp, 1])

    if factorization_list==[]:
        factorization_list.append([n, 1])

    return factorization_list


if __name__ == "__main__":
    N = int(input())

    if N == 1:
        print(0)

    else:
        factorization_list = factorization(N)
        count = 0
        for factor in factorization_list:
            e = factor[1]
            i = 1
            while True:
                e -= i
                i += 1
                count += 1
                if e < i:
                    break
        print(count)

Buggy python submission (verdict: Time Limit Exceeded):
import math

def isPrime(num):
    if num < 2:
        return False
    elif num == 2:
        return True
    elif num % 2 == 0:
        return False

    for i in range(3, math.floor(math.sqrt(num))+1, 2):
        if num % i == 0:
            return False
    return True


def find_all_prime(num):
    prime_list = [2]
    for i in range(3, num, 2):
        if isPrime(i):
            prime_list.append(i)

    return prime_list


if __name__ == "__main__":
    N = int(input())
    if isPrime(N):
        print(1)
    else:      
        prime_list = find_all_prime(2*10**6)
        count = 0  
        for i in prime_list:
            j = 1
            while N > 1:
                if N // i**j == 0:
                    break
                if N % i**j == 0:
                    N = N // i**j
                    count += 1
                j +=1
        
        print(count)

Fixed submission:
def factorization(n):
    factorization_list = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp % i == 0:
            count = 0
            while temp % i == 0:
                count += 1
                temp //= i
            factorization_list.append([i, count])

    if temp != 1:
        factorization_list.append([temp, 1])

    if factorization_list==[]:
        factorization_list.append([n, 1])

    return factorization_list


if __name__ == "__main__":
    N = int(input())

    if N == 1:
        print(0)

    else:
        factorization_list = factorization(N)
        count = 0
        for factor in factorization_list:
            e = factor[1]
            i = 1
            while True:
                e -= i
                i += 1
                count += 1
                if e < i:
                    break
        print(count)