Products

Let n be a positive integer. George wrote a program which finds positive integers a1, a2, …, ak, which product increases n times if we add 1 to each of them, i.d. 

(a1+1)(a2+1)...(ak+1) = na1a2...ak.

Now, however, he wants to find out what’s the smallest value of k, for which this is possible. Write a program mink, which solves the George’s new task.

From the first line of the standard input it is given n (2 < n < 1000).

On a line of the standard output the program must write the searched value of k.