Distinct Subarray GCDs

For a sequence $A$ of length $n$, define $f(lo, hi)$ as the GCD of $A_{lo}$ through $A_{hi}$ (indices, not values). Count how many distinct values $f(lo, hi)$ can take.

Multiple test cases. Each starts with n$$(1 \le n \le 100000), then $n$ lines each with an element a$$(1 \le a \le 100). Input ends when $n = 0$.

For each test case, print the number of distinct GCD values on one line.