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5 초 512 MB 30 24 24 80.000%

## 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

• 1 ≤ T ≤ 100.
• 1 ≤ K ≤ 105.

## 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.

## 예제 입력 1

4
1
2
3
10


## 예제 출력 1

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


## 채점 및 기타 정보

• 예제는 채점하지 않는다.