A Fi-binary number is a number that contains only 0 and 1. It does not contain any leading 0. And also it does not contain 2 consecutive 1. The first few such number are 1, 10, 100, 101, 1000, 1001, 1010, 10000, 10001, 10010, 10100, 10101 and so on. You are given n. You have to calculate the nth Fi-Binary number.
Input
Input starts with an integer T (≤ 10000), denoting the number of test cases.
Each case contains an integer n (1 ≤ n ≤ 109).
Output
For each case, print the case number and the nth Fi-Binary number
Sample
| Sample Input | Sample Output |
|---|---|
4 10 20 30 40 | Case 1: 10010 Case 2: 101010 Case 3: 1010001 Case 4: 10001001 |