Run, Run, Runaround Numbers

Time Limit: 10 Seconds
Memory Limit: 32768 KB

An N-digit runaround number is characterized as follows:

It is an integer with exactly N digits, each of which is between 1 and 9,
inclusively.

The digits form a sequence with each digit telling where the next digit in the
sequence occurs. This is done by giving the number of digits to the right of
the digit where the next digit in the sequence occurs. If necessary, counting
wraps around from the rightmost digit back to the leftmost.

The leftmost digit in the number is the first digit in the sequence, and the
sequence must return to this digit after all digits in the number have been
used exactly once.

No digit will appear more than once in the number.

For example, consider the number 81362. To verify that this is a runaround number,
we use the steps shown below:

1. Start with the leftmost digit, 8: 1 3 6 2

2. Count 8 digits to the right, ending on 6 (note the wraparound): 1 3 2

3. Count 6 digits to the right, ending on 2: 1 3

4. Count 2 digits to the right, ending on 1: 3

5. Count 1 digit to the right, ending on 3:

6. Count 3 digits to the right, ending on 8 (where we began):

**Input and Output**

In this problem you will be provided with one or more input lines, each with
a single integer R having between 2 and 7 digits followed immediately by the
end of line. For each such number, determine the smallest runaround number that
is equal to or greater than R. There will always be such a number for each of
the input numbers. Display the resulting number in the format illustrated below.
The last line of the input will contain only the digit 0 in column 1.

**Sample Input**

12

123

1234

81111

82222

83333

911111

7654321

0

**Sample Output**

Case 1: 13

Case 2: 147

Case 3: 1263

Case 4: 81236

Case 5: 83491

Case 6: 83491

Case 7: 913425

Case 8: 8124956

Source:

**North Central North America 1996**
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