Exponential Towers
The number 729 can be written as a power in several ways: 3^6, 9^3 and 27^2. It can be written as 729^1, of course, but that does not count as a power. We want to go some steps further. To do so, it is convenient to use ^ for exponentiation, so we define a^b = a^b. The number 256 then can be also written as 2^2^3, or as 4^2^2. Recall that ^ is right associative, so 2^2^3 means 2^(2^3).
We define a tower of powers of height k to be an expression of the form a[1]^a[2]^a[3]^.. ^a[k], with k > 1, and integers a[i] > 1.
Given a tower of powers of height 3, representing some integer n, how many towers of powers of height at least 3 represent n?
Input
Contains several test cases, each on a separate line. Each test case has the form a^b^c, where a, b and c are integers, 1 < a, b, c ≤ 9585.
Output
For each test case, print the number of ways the number n = a^b^c can be represented as a tower of powers of height at least three.
The magic number 9585 is carefully chosen such that the output is always less than 2^63.