N'th Lucky Number

Time Limit: 1 sec

 

The Problem

Lucky numbers consist of exactly those positive integers which are powers of 7 (such as 7⁰ = 1 and 7³ = 343) and those that are a sum of unique powers of 7 (such as 50 = 7⁰ + 7² or 56 = 7¹ + 7², but not 14 = 7¹ + 7¹). The sequence

 

1, 7, 8, 49, 50, 56, 57, 343, 344, 350

 

shows the first 10 lucky numbers.

 

Given an integer number N, you need to find the N^th lucky number.

 

The Input

The first line contains an integer number T, which indicates the number of test cases (0<T<10000). Each test case is given in one line. This line contains a positive integer number N (0<N<60000).

 

The Output

For each test case, print a single line “Case X: L”, here X is the case number start from 1 to T and L is the N^th lucky number.

 

Sample Input

3

1

4

6

 

Sample Output

Case 1: 1

Case 2: 49

Case 3: 56

 

 

 

[School & College Level]

Inter School & College Programming Contest (ISCPC) 2017

Problem Setter: Shahin ShamS