## Description

Whenever we think of sorting integers, we tend to think of sorting them in ascending or descending order. However, we can play around a bit and define new sorting criteria. One criterion could be sorting numbers in terms of their summation of digits. Therefore in this sorting criterion, 13 would come before 9 as sum of the digits of 13 is 4 and that of 9 is 9. In this problem, we are concerned with sorting numbers in the range 1 to 2000000 with the following sorting criteria. Numbers in this range must be sorted in terms of the number of factors in their prime factorization. Incase of a tie, the smaller number will come first. For example, 20 = 2*2*5, so it has 3 numbers in its prime factorization. Similarly 35 = 5*7 has 2 numbers in its prime factorization. Therefore, 35 will come before 20 according to this criterion.## Input

Each case of input will consist of a positive integer n<=2000000. The last case is followed by a 0. Total number of test cases can be as large as 100000.## Output

For each case of input, there will be one line of output. It will consist of the case number followed by the nth number in the range 1 to 2000000 after the sorting rule has been applied. Look at sample output for further clarification.## Sample Input

1 2 3 4 0## Sample Output

Case 1: 1 Case 2: 2 Case 3: 3 Case 4: 5## Source

Shamim Hafiz @ Next generation contest ¨C 4 @ UVA