12582번 - Your Rank is Pure (Large) 다국어

Pontius: You know, I like this number 127, I don't know why.
Woland: Well, that is an object so pure. You know the prime numbers.
Pontius: Surely I do. Those are the objects possessed by our ancient masters hundreds of years ago. Oh, yes, why then? 127 is indeed a prime number as I was told.
Woland: Not... only... that. 127 is the 31st prime number; then, 31 is itself a prime, it is the 11th; and 11 is the 5th; 5 is the 3rd; 3, you know, is the second; and finally 2 is the 1st.
Pontius: Heh, that is indeed... purely prime.

The game can be played on any subset S of positive integers. A number in S is considered pure with respect to S if, starting from it, you can continue taking its rank in S, and get a number that is also in S, until in finite steps you hit the number 1, which is not in S.

When n is given, in how many ways you can pick S, a subset of {2, 3, ..., n}, so that n is pure, with respect to S? The answer might be a big number, you need to output it modulo 100003.

The first line of the input gives the number of test cases, T.  T lines follow. Each contains a single integer n.

Limits

• T ≤ 100.
• 2 ≤ n ≤ 500.

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is the answer as described above.