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"
• ...
• S_N = S_N-1 + "0" + switch(reverse(S_N-1)).

You need to figure out the Kth character of S_googol, 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 S_googol.

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