The proper divisors of a number n are all the positive divisors of n that are smaller than n. For instance, the proper divisors of 20 are 1, 2, 4, 5, and 10. In this problem, we will say that a number is pseudoperfect if it can be obtained by adding up some of (or all) its proper divisors. For instance, 20 is pseudoperfect, because 1 + 4 + 5 + 10 = 20.
Write a program that, for every given number n,
Input
Input consists of several strictly positive natural numbers.
Output
For every given n, print its number of proper divisors, if this is larger than 15. Otherwise, tell if n is pseudoperfect or not. Follow the format of the example.
Input
1 6 10 20 210 2310 65536 1000000000 999999996 999999937 999999936
Output
1 : NOT pseudoperfect 6 : pseudoperfect 10 : NOT pseudoperfect 20 : pseudoperfect 210 : pseudoperfect 2310 : 31 proper divisors 65536 : 16 proper divisors 1000000000 : 99 proper divisors 999999996 : pseudoperfect 999999937 : NOT pseudoperfect 999999936 : 167 proper divisors