# Easy Sequence 1

Limits 1s, 512 MB

Let’s define an easy sequence $F$. Where:

$F(1)=1$

$F(2X) = F(X)^2 + 1$

$F(2X+1) = F(X) \times F(X+1) + 2$

Here $X$ is a positive integer. The first few elements of the sequence are 1, 2, 4, 5, 10, 17, 22, 26, 52, 101.

Now given a value of $F(X)$, can you compute $X$?

## Input

The first line of the input is a positive integer $T$ ($T ≤ 100$), the number of test cases. Then $T$ lines follow.

In each line there will be a value of $F(X)$ ($1 ≤ F(X) ≤ 10^9$). It is guaranteed that for every $F(X)$ in the input, there exists a valid $X$.

## Output

For each case print a line in $\texttt{Case I: X}$ format where $\texttt{I}$ is the test case number and $\texttt{X}$ is the corresponding value for the given $F(X)$ in the input.

## Sample

InputOutput
10
1
2
4
5
10
17
22
26
52
101

Case 1: 1
Case 2: 2
Case 3: 3
Case 4: 4
Case 5: 5
Case 6: 6
Case 7: 7
Case 8: 8
Case 9: 9
Case 10: 10