Alien Generator

Problem

Astronauts have landed on a new planet, Kickstartos. They have discovered a machine on the planet: a generator that creates gold bars.

The generator works as follows. On the first day, an astronaut inputs a positive integer $K$ into the generator. The generator will produce $K$ gold bars that day. The next day, it will produce $K+1$, the following day, $K+2$, and so on. Formally, on day $i$, the generator will produce $K+i-1$ gold bars.

However, the astronauts also know that there is a limitation to the generator:
if on any day, the generator would end up producing more than $\mathbf{G}$ gold bars in total across all the days, then it will break down on that day and will produce $0$ gold bars on that day and thereafter. The astronauts would like to avoid this, so they want to produce exactly $\mathbf{G}$ gold bars.

Consider $K=2$ and $\mathbf{G}=8$. On day $1$, the generator would produce $2$ gold bars. On day $2$, the generator would produce $3$ more gold bars making the total gold bars is equal to $5$. On day $3$, the generator would produce $4$ more gold bars which would lead to a total of $9$ gold bars. Thus, the generator would break on day $3$ before producing $4$ gold bars. Hence, the total number of gold bars generated is $5$ in this case.

Formally, for a given $\mathbf{G}$, astronauts would like to know how many possible values of $K$ on day $1$ would eventually produce exactly $\mathbf{G}$ gold bars.

Input

The first line of the input gives the number of test cases, $\mathbf{T}$. $\mathbf{T}$ lines follow.
Each line contains a single integer $\mathbf{G}$, representing the maximum number of gold bars the generator can generate.

Output

For each test case, output one line containing Case #$x$: $y$, where $x$ is the test case number (starting from $1$) and $y$ is the number of possible values of $K$ on day $1$ that would eventually produce exactly $\mathbf{G}$ gold bars.

Limits

Time limit: 30 seconds.
Memory limit: 1 GB.
$1 \le \mathbf{T} \le 100$

Test Set 1

$1 \le \mathbf{G} \le 10^4$.

Test Set 2

$1 \le \mathbf{G} \le 10^{12}$ for at most $20$ test cases.
For the remaining cases, $1 \le \mathbf{G} \le 10^4$.

Sample

Sample Input

2
10
125

Sample Output

Case #1: 2
Case #2: 4

For Sample Case #1, there are $2$ possible values of $K$ $(1,10)$ that would eventually produce exactly $10$ gold bars. For $K=1$, we will have $1+2+3+4=10$ gold bars after $4$ days, and for $K=10$, we will have $10$ gold bars after just $1$ day.

For Sample Case #2, there are $4$ possible values of $K$ $(8,23,62,125)$ that would eventually produce exactly $125$ gold bars.