A positive integer N can be the LCM (Least Common Multiple) of different set of numbers. For example, LCM(6,24) = 24, LCM(12,8) = 24, LCM(1,2,3,4,8) = 24, etc. For a given number N, maximum sum LCM indicates the set of numbers whose LCM is N and summation is maximum. Let, MSLCM(N) denote this maximum sum of numbers. Given the value of N you will have to find the value: ∑N MSLCM(i) i=2 Obviously, in a set the same value never comes twice. Input Input file contains at most 200 lines. Each line contains a positive integer which denotes the value of N (1 < N < 20000001). Input is terminated by a line containing a single zero, which should not be processed. Output For each positive number N in the input, produce one line of output. This line contains an integer which denotes the value ΣNi=2MSLCM(i) Sample Input 10 1000 0 Sample Output 86 823080