Problem

I have a string S consisting of lower-case alphabetic characters, 'a' - 'z'. Each maximal sequence of contiguous characters that are the same is called a "run". For example, "bookkeeper" has 7 runs. How many different permutations of S have exactly the same number of runs as S?

Two permutations a and b are considered different if there exists some index i at which they have a different character: a[i] ≠ b[i].

Input

The first line of the input gives the number of test cases, T. T lines follow. Each contains a single non-empty string of lower-case alphabetic characters, S, the string of interest.

Output

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is the number of different permutations of S that have exactly the same number of runs as S, modulo 1000003.

Limits

1 ≤ T ≤ 100.

S is at least 1 character long.

Memory limit: 1GB.

Small dataset (Test set 1 - Visible; 14 Points)

S is at most 100 characters long.

Time limit: 30 6 seconds.

Large dataset (Test set 2 - Hidden; 16 Points)

S is at most 450000 characters long.

S has at most 100 runs.

The input file will not exceed 1 megabyte in size.

Time limit: 60 12 seconds.

Sample

2
aabcd
bookkeeper

Case #1: 24
Case #2: 7200