Problem:
 Score : 400 points    Problem Statement  Given is a positive integer N . Consider repeatedly applying the operation below on N :   First, choose a positive integer z satisfying all of the conditions below:  z can be represented as z=p^e , where p is a prime number and e is a positive integer;  z divides N ;  z is different from all integers chosen in previous operations.    Then, replace N with N/z .   Find the maximum number of times the operation can be applied.      Constraints   All values in input are integers.  1 \leq N \leq 10^{12}         Input  Input is given from Standard Input in the following format:  N       Output  Print the maximum number of times the operation can be applied.        Sample Input 1 24      Sample Output 1 3  We can apply the operation three times by, for example, making the following choices:   Choose z=2 (=2^1) . (Now we have N=12 .)  Choose z=3 (=3^1) . (Now we have N=4 .)  Choose z=4 (=2^2) . (Now we have N=1 .)        Sample Input 2 1      Sample Output 2 0  We cannot apply the operation at all.       Sample Input 3 64      Sample Output 3 3  We can apply the operation three times by, for example, making the following choices:   Choose z=2 (=2^1) . (Now we have N=32 .)  Choose z=4 (=2^2) . (Now we have N=8 .)  Choose z=8 (=2^3) . (Now we have N=1 .)        Sample Input 4 1000000007      Sample Output 4 1  We can apply the operation once by, for example, making the following choice:   z=1000000007 (=1000000007^1) . (Now we have N=1 .)        Sample Input 5 997764507000      Sample Output 5 7

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz') 
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    
    
    
    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        
        
        
        
        
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    
    
    N = r_int()
    l = [0] * 40
    cur = 0
    upd = 1
    cnt = 0
    for i, ll in enumerate(l):
        j = i + 1
        if cur + upd <= j:
            cnt += 1
            cur = cur + upd
            upd += 1
            l[i] = cnt
        else:
            l[i] = cnt
    
    def factorization(n):
        arr = []
        temp = n
        for i in range(2, int(-(-n**0.5//1))+1):
            if temp%i==0:
                cnt=0
                while temp%i==0:
                    cnt+=1
                    temp //= i
                arr.append([i, cnt])

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

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

        return arr

    q = factorization(N) 
    ans = 0
    for q1, q2 in q:
        ans += l[q2-1]
    if N == 1:
        print(0)
    else:
        print(ans)
    
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
import sys
from bisect import bisect_right
n = int(input())
data = [n*(n+1)//2 for n in range(1,40)]
cnt2 = 0
while n % 2 == 0:
    cnt2 += 1
    n //= 2
ans = bisect_right(data,cnt2)
if n == 1:
    print(ans)
    sys.exit()
for i in range(3,int(n**(0.5))+1,2):
    cnt = 0
    while n % i == 0:
        cnt += 1
        n //= i
    ans += bisect_right(data,cnt)
    if n == 1:
        break
else:
    ans += 1
print(ans)

Solution (Python):
N = int(input())

def prime_factorize(n):
    if n == 1:
        return []
    ans = []
    tmp = n
    i = 2
    while pow(i, 2) <= n:
        if tmp % i == 0:
            cnt = 0
            while tmp % i == 0:
                cnt += 1
                tmp /= i
            ans.append([i, cnt])
        i += 1
    if tmp != 1:
        ans.append([tmp, 1])
    if ans == []:
        ans.append([n, 1])
    return ans

pl = prime_factorize(N)
ans = 0
for p, n in pl:
    tmp = n
    i = 1
    while tmp-i >= 0:
        tmp -= i
        i += 1
        ans += 1
print(ans)

Solution (Python):
import collections,sys
def I(): return int(sys.stdin.readline().rstrip())
N = I()
def primeFactor(num):
    prime_factor = collections.defaultdict(int)
    for i in range(2,int(num**0.5)+1):
        while num%i==0:
            prime_factor[i] += 1
            num //= i
    if num>1:
        prime_factor[num]=1
    return prime_factor
sequence = []
for i in range(1,50):
    sequence.append(i*(i+1)//2)
ans = 0
for v in primeFactor(N).values():
    for j,x in enumerate(sequence,1):
        if v<x:
            ans += j-1
            break
print(ans)

Solution (Python):
import sys
import  math
from heapq import *
import fractions
from collections import defaultdict
stdin = sys.stdin
     
ns = lambda: stdin.readline().rstrip()
ni = lambda: int(stdin.readline().rstrip())
nm = lambda: map(int, stdin.readline().split())
nl = lambda: list(map(int, stdin.readline().split()))


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

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

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

    return arr


N=int(input())
mod_l=factorization(N)
ans=0

if(N==1):
    print(0)
    sys.exit(0)
    
for i in mod_l:
    tmp=i[1]
    c=1
    while(c<=tmp):
        tmp-=c
        c+=1
        ans+=1

print(ans)

Solution (Python):
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a


import collections
n = int(input())
if n == 1:
    print(0)
    exit()
c = collections.Counter(prime_factorize(n))
t = sorted(c.values())
max_c = max(t)
calc_list = []
ans = 0
a = 0
i = 1
while a <= max_c:
    a = i * (i + 1) // 2
    while t[0] < a:
        ans += i - 1
        t.pop(0)
        if len(t) == 0:
            break
    i += 1
print(ans)

Solution (Python):
n = int(input())
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

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

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

    return arr

a = factorization(n)

ans = 0
for i in range(len(a)):
    e = a[i][1]
    j = 1
    while e - j >= 0:
        e -= j
        j += 1
        ans += 1

if n == 1:
    print(0)
else:
    print(ans)

Solution (Python):
from collections import Counter


def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

n = int(input())

li = prime_factorize(n)

c = Counter(li)

ans = 0
for v in c.values():
  num = 1
  cnt = 2
  while v >= num:
    ans += 1 
    num += cnt
    cnt += 1



print(ans)

Solution (Python):
from itertools import count

n = int(input())

prime_factor = {}
while n % 2 == 0:
    prime_factor[2] = prime_factor.get(2, 0) + 1
    n //= 2
f = 3
while f * f <= n:
    if n % f == 0:
        prime_factor[f] = prime_factor.get(f, 0) + 1
        n //= f
    else:
        f += 2
if n != 1:
    prime_factor[n] = prime_factor.get(n, 0) + 1

res = 0
for v in prime_factor.values():
    for i in count(1):
        if i > v:
            break
        res += 1
        v -= i

print(res)

Solution (Python):

import sys


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

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

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

    return arr

def solve(N: int):
    factors = factorization(N)
    if N == 1:
        print(0)
        return
    result = 0
    for _, n in factors:
        cnt = 0
        while True:
            s = cnt * (cnt + 1) // 2
            if s > n:
                cnt -= 1
                break
            cnt += 1
        result += cnt
    print(result)


    return



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    solve(N)

if __name__ == '__main__':
    main()

Solution (Python):

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

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

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

    return arr

f=factorization(int(input())) 
ans=0
for list in f:
  if list[0]==1:
    continue
  m=list[1]
  n=int((2*m)**(1/2))
  while True:
    if n*(1+n)>2*m:
      n-=1
      break
    n+=1

  ans+=n
print(ans)

Solution (Python):
N=int(input())
if N==1:
  print(0)
  exit()
  
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

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

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

    return arr

a=factorization(N) 
A=[]
d=0
for i in range(1,50):
  d+=i
  A.append(d)
import bisect
cnt=0
for x,y in a:
  e=bisect.bisect_right(A,y)
  cnt+=e
print(cnt)

Solution (Python):
from bisect import bisect_right

N = int(input())
Nroot = int(N**(1/2))

an = [i*(i+1)//2 for i in range(50)]

ans = 0
for i in range(2, Nroot):
  count = 0
  if N%i == 0:
    Ni = N//i
    count = 1
    while Ni%i == 0:
      count += 1
      Ni = Ni//i
      
    ans += bisect_right(an, count) -1
    
  N = N//(i**count)
  
if N>1:
  print(ans+1)
else:
  print(ans)

Solution (Python):

pf={}
m=int(input())
for i in range(2,int(m**0.5)+1):
    while m%i==0:
        pf[i]=pf.get(i,0)+1
        m//=i
if m>1:pf[m]=1
ans = 0
for v in pf.values():
    now = v
    cou = 1
    while True:
        if now - cou >= 0:
            ans += 1
            now -= cou
            cou += 1
        else:
            break
print(ans)

Solution (Python):
import collections
import bisect
n = int(input())

primes = []
a = 2
while n > a*a:
    while n % a == 0:
        primes.append(a)
        n //= a
    a += 1
if n != 1:
    primes.append(n)

ctr = collections.Counter(primes)
ans = 0
for k,v in ctr.items():
    for i in range(1,100):
        if v >= i*(i+1)//2:
            ans += 1
print(ans)

Solution (Python):
n = int(input())
n2 = int(n**0.5//1)

def div(n,p):
    cnt = 0
    a = 1
    while n%p == 0:
        n = n//p
        cnt += 1
        if cnt == a:
            cnt = 0
            a += 1
    return [n,a-1]

ans = 0
for z in range(2,n2):
    if n%z == 0:
        n,cur = div(n,z)
        ans += cur

if n != 1: ans += 1

print(ans)

Solution (Python):

def fctr1(n):
    f = {}
    c = 0
    r = int(n**0.5)
    for i in range(2, r+2):
        while n % i == 0:
            c += 1
            n = n//i
        if c != 0:
            f[i] = c
            c = 0
    if n != 1:
        f[n] = 1
    return f


N = int(input())
p = fctr1(N)
ans = 0
for k, v in p.items():
    c = 0
    while (v-c-1) >= 0:
        c += 1
        v -= c
    ans += c

print(ans)

Solution (Python):
n = int(input())
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a
a = prime_factorize(n)
counter = 0
for i in set(a):
    cou = a.count(i)
    tmp = 0
    j = 1
    while tmp < cou:
        tmp += j
        j += 1
        if tmp <= cou:
            counter += 1
print(counter)

Solution (Python):
from bisect import bisect_right,bisect

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

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

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

    return arr
  
N = int(input())


def triangle(n):
  return n*(n+1)//2

T = [ triangle(i) for i in range(1, 10**6)]



ans = 0
for _, i in factorization(N):
  ans += bisect_right(T, i) 

  
  
if N == 1:
  ans = 0
print(ans)

Solution (Python):


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

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

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

    return arr
n = int(input())
arr = factorization(n)

if(n==1):
    print(0)
    exit()
ans = 0
for i in arr:
    for j in range(1,1000):
        if(i[1]+1<=j*(j+1)//2):
            ans += j-1
            break

print(ans)

Solution (Python):
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

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

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

    return arr

import sys
N = int(input())
if N == 1:
    print(0)
    sys.exit()
A = factorization(N)
ans = 0
for i in range(len(A)):
    for j in range(1,A[i][1]+1):
        if N % A[i][0]**j == 0:
            ans += 1
            N //= A[i][0]**j
        else:
            break

print(ans)

Solution (Python):

import numpy as np


def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

N = int(input())



primes = prime_factorize(N)

prime2num = {}
for prime in primes:
    if prime in prime2num:
        prime2num[prime] += 1
    else:
        prime2num[prime] = 1

ans = 0
for prime, num in prime2num.items():
    i = 1
    c = 0
    while True:
        c += i
        if c > num:
            break
        i += 1
        ans += 1
        
print(ans)

Solution (Python):
import math
l = []
n = int(input())
for i in range(2,int(math.sqrt(n))+1):
  flg = 0
  while n % i == 0:
    if flg == 0:
      l.append(1)
      flg = 1
    else:
      l[-1] += 1
    n = n//i

if n != 1:
  l.append(1)

ans = 0
for i in range(len(l)):
  c = 1
  while l[i] - c >= 0:
    l[i] -= c
    c += 1
    ans += 1

print(ans)

Solution (Python):
def primeFactorize(n):
    fac = []
    if n < 2: return fac
    while n%2 == 0:
        n //= 2
        fac.append(2)
    for i in range(3,int(n**0.5)+1,2):
        while n%i == 0:
            n //= i
            fac.append(i)
    if n != 1: fac.append(n)
    return fac

n = int(input())
s = set()
ans = 0
x = 1
p = -1
for f in primeFactorize(n):
    if p != f: x = 1
    x *= f
    p = f
    if x not in s:
        ans += 1
        s.add(x)
        x = 1
print(ans)

Solution (Python):
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

N = int(input())
n_root = prime_factorize(N)
n_set = list(set(n_root))

ans = 0
for num in n_set:
    item = n_root.count(num)
    i = 1
    while item >= i:
        item -= i
        ans += 1
        i += 1

print(ans)

Solution (Python):
from collections import defaultdict
from functools import lru_cache
from bisect import bisect_right as bir
from collections import Counter
N = int(input())


def prime(n):
    ret = []
    while n % 2 == 0:
        ret.append(2)
        n //= 2

    f = 3
    while f*f <= n:
        if n % f == 0:
            ret.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        ret.append(n)
    return ret


D = Counter(prime(N))

comb = []
m = 0
for i in range(1, 10000):
    m += i
    comb.append(m)


ans = 0
for k, v in D.items():
    ans += bir(comb, v)

print(ans)