You are given a positive integer $n$ greater or equal to $2$. For every pair of integers $a$ and $b$ ($2 \le |a|, |b| \le n$), you can transform $a$ into $b$ if and only if there exists an integer $x$ such that $1 < |x|$ and ($a \cdot x = b$ or $b \cdot x = a$), where $|x|$ denotes the absolute value of $x$.

After such a transformation, your score increases by $|x|$ points and you are not allowed to transform $a$ into $b$ nor $b$ into $a$ anymore.

Initially, you have a score of $0$. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?


-----Input-----

A single line contains a single integer $n$ ($2 \le n \le 100\,000$) — the given integer described above.


-----Output-----

Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print $0$.


-----Examples-----
Input
4

Output
8
Input
6

Output
28
Input
2

Output
0


-----Note-----

In the first example, the transformations are $2 \rightarrow 4 \rightarrow (-2) \rightarrow (-4) \rightarrow 2$.

In the third example, it is impossible to perform even a single transformation.

Difficulty: interview

Starter code:

Solutions:
#      
import collections, atexit, math, sys, bisect 

sys.setrecursionlimit(1000000)
def getIntList():
    return list(map(int, input().split()))    

try :
    #raise ModuleNotFoundError
    import numpy
    def dprint(*args, **kwargs):
        #print(*args, **kwargs, file=sys.stderr)
        # in python 3.4 **kwargs is invalid???
        print(*args,  file=sys.stderr)
    dprint('debug mode')
except Exception:
    def dprint(*args, **kwargs):
        pass



inId = 0
outId = 0
if inId>0:
    dprint('use input', inId)
    sys.stdin = open('input'+ str(inId) + '.txt', 'r') #标准输出重定向至文件
if outId>0:
    dprint('use output', outId)
    sys.stdout = open('stdout'+ str(outId) + '.txt', 'w') #标准输出重定向至文件
    atexit.register(lambda :sys.stdout.close())     #idle 中不会执行 atexit
    
N, = getIntList()
#print(N)
re = 0
for i in range(2,N):

    t = N // i -1
    re += t * i

print(re *4)








def ii():
    return int(input())
def mi():
    return map(int, input().split())
def li():
    return list(mi())

n = ii()
ans = 0
for i in range(2, n):
    for j in range(2 * i, n + 1, i):
        ans += j // i
print(ans * 4)

import sys
n=int(input())

if n<=3:
    print(0)
    return

score=0
import math
def score(x):
    ANS=0
    xr=math.ceil(math.sqrt(x))

    LIST=[]
    for i in range(1,xr+3):
        if x%i==0:
            LIST.append(i)
            LIST.append(x//i)

    LIST=sorted(list(set(LIST)))

    for l in LIST[1:-1]:
        ANS+=x//l

    return ANS

ANS=0
for i in range(4,n+1):
    ANS+=score(i)

print(ANS*4)
    



i = input()
i = int(i)
v = 0
g = 2
s = 4
while g <= i:
	while s <= i:
		v = v + int(s / g * 4)
		s = s + g
	g = g + 1
	s = g * 2
print(str(v))

n = int(input())
r = 0
i = 2
while i*2 <=n:
	a = int(n/i)
	r += (a+2)*(a-2+1)/2
	i += 1
print(int(4*r))


n = int(input())
sum = 0

for i in range(2, n + 1):  
  j = 2
  while(j * i <= n):
    sum += i
    j += 1
print(4 * sum)

from math import sqrt, floor, ceil
n = int(input())

ran = list(range(2, 1+n//2))
xx = [ d*(n//d-1)     for d in ran]
print(sum(xx)*4)


n = int(input())
ans = 0
for i in range(2, n + 1):
    for j in range(i + i, n + 1, i):
        ans += 4 * j // i
print(ans)


n = int(input())
rang = list(range(2,n//2+1))
a = [i*(n//i-1) for i in rang]
print(sum(a)*4)


n = int(input())
print(4 * sum(x*((n-x)//x) for x in range(2, n)))



# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 11/19/18

"""

N = int(input())

ans = 0
for i in range(2, N+1):
    ans += 4 * i * (N//i-1)
print(ans)

n=int(input())
ans=0
if(n<4):
	print('0')
	return
for i in range(2,(n//2)+1):
	k=n//i;
	ans+=(k*(k+1))//2-1
print(4*ans)

n=int(input())
print(4*sum(i*(n//i-1) for i in range(2,n)))

from sys import *
n = int(stdin.readline())
ans = 0
for i in range(2,n+1):
    for j in range(i*2,n+1,i):
        ans += 4 * (j // i)
print(ans)


n = int(input())

ans = 0
for i in range(2,n//2+1):
    x = n // i 
    ans +=  ( x * (x+1) // 2 - 1 ) * 4
print(ans)    


n=int(input())
ans=0
for i in range(2,n+1):
	for j in range(2*i,n+1,i):
		ans+=(4*(j//i))
print(ans)

n = int(input())
res = 0
for i in range(n-2):
    if int(n/(i+2)-1):
        res += 4*(i+2)*int(n/(i+2)-1)
print(res)


n=int(input())
ans=0
if(n==2 or n==3):
	print(0)
else:
	i=2
	while(i<=n):
		j=2
		num=n//i
		ans+=(2*num*(num+1))
		ans-=4
		i+=1
		#print(2*j*(j+1))
	print(ans)


n=int(input())
ans=0
if(n==2 or n==3):
	print(0)
else:
	i=2
	while(i<=n):
		j=2
		while(j*i<=n):
			ans+=(j*4)
			j+=1
		i+=1
	print(ans)


class IntegersFun():
    def __init__(self, n):
        self.n = n

    def get_value(self):
        sm = 0
        for i in range(2,self.n+1):
            for j in range(2*i, self.n+1, i):
                sm += 4*j/i
        return int(sm)

n = int(input())
print(IntegersFun(n).get_value())

# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
from sys import stdin, stdout
import collections

N = int(input())
#s = input()
#N,Q = [int(x) for x in stdin.readline().split()]

res = 0
for m in range(2,N+1):
    d = N//m
    d -= 1
    res += d*m
    
    if d==0:
        break
    
print(4*res)

from sys import stdin
from collections import deque
mod = 10**9 + 7
import sys
sys.setrecursionlimit(10**5)
from queue import PriorityQueue
# def rl():
#     return [int(w) for w in stdin.readline().split()]
from bisect import bisect_right
from bisect import bisect_left
from collections import defaultdict
from math import sqrt,factorial,gcd,log2,inf,ceil
# map(int,input().split())
# # l = list(map(int,input().split()))
# from itertools import permutations
import heapq
# input = lambda: sys.stdin.readline().rstrip()
input = lambda : sys.stdin.readline().rstrip()
from sys import stdin, stdout
from heapq import heapify, heappush, heappop


n = int(input())

ans = 0

for i in range(2,n+1):
    ans+=i*(n//i - 1)

print(ans*4)




n = int(input())
print(sum([i * (int(n / i) - 1) for i in range(2, n + 1)]) * 4)

# run : python wtf.py


n = int(input())

ans = 0
for i in range(2, n + 1):
    cur = n // i
    if cur == 1:
        continue
    summ = (cur + 2) * (cur - 1) // 2
    ans += summ

print(ans * 4)


n = int(input())
ans = 0
for i in range(2, n + 1):
    for j in range(i + i, n + 1, i):
        ans += 4 * j // i
print(ans)