# Googol String (Large)

## 문제

A "0/1 string" is a string in which every character is either `0` or `1`. There are two operations that can be performed on a 0/1 string:

- switch: Every `0` becomes `1` and every `1` becomes `0`. For example, "100" becomes "011".
- reverse: The string is reversed. For example, "100" becomes "001".

Consider this infinite sequence of 0/1 strings:

- S0 = ""
- S1 = "0"
- S2 = "001"
- S3 = "0010011"
- S4 = "001001100011011"
- ...
- SN = SN-1 + "0" + switch(reverse(SN-1)).

You need to figure out the Kth character of Sgoogol, where googol = 10100.

## 입력

The first line of the input gives the number of test cases, T. Each of the next T lines contains a number K.

## 출력

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 Kth character of Sgoogol.

## 제한

- 1 ≤ T ≤ 100.
- 1 ≤ K ≤ 1018.

## 예제 입력 1 복사

    4
    1
    2
    3
    10

## 예제 출력 1 복사

    Case #1: 0
    Case #2: 0
    Case #3: 1
    Case #4: 0