Problem: Given a positive integer K > 2, with prime
factorization:

K = p1^a1 * p2^a2 ... * pn^an

Compute the following:

S = a1*p1 + a2*p2 ... + an*pn.


Input
A list of 
Output
For each integer compute the super factor
sum and output it on a single line.

Example

Input:
6
7
Output:
5
7

Solution (in PYTHON):

Solution:
import random
import os
yash=(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997)

def fix(m):
    for ai in yash:
        if m%ai==0:
            return ai
    return m

def rabin_miller(a,i,n):
    if i==0:
        return 1
    x=rabin_miller(a,i/2,n)
    if x==0:
        return 0
    y=(x*x)%n
    if (y==1)and(x<>1)and(x<>n-1):
        return 0
    if i%2<>0:
        y=(a*y)%n
    return y

def gcd(x,y):
    if y==0:
        return x
    return gcd(y,x%y)

def brent_rho(n):
    if (n<=3)or(rabin_miller(random.randint(2,n-2),n-1,n)==1):
        return n
    y,r,q,m=1,1,1,203
    while 1:
        x=y
        for i in range(1,r+1):
            y=(y*y+1)%n
        k=0
        while 1:
            ys=y
            for i in range(1,min(m,r-k)+1):
                y=(y*y+1)%n
                q=(q*abs(x-y))%n
            g=gcd(q,n)
            k+=m
            if (k>=r)or(g>1):
                break
        r*=2
        if g>1:
            break
    if g==n:
        while 1:
            ys=(ys*ys+1)%n
            g=gcd(abs(x-ys),n)
            if g>1:
                break
    if g==n:
        return n
    return brent_rho(g)

def divsum2(n):
    if n==1:
        return 0
    d=brent_rho(n)
    d=fix(d)
    assert (d<=3)or(rabin_miller(random.randint(2,d-2),d-1,d)==1)
    f,m=0,n
    while m%d==0:
        m/=d
        f = f + 1;
    return (f*d)+(divsum2(m))

try:
    while(1):
	    z=input()
	    print divsum2(z)
except:
	os.sys.exit(0);