Paradoxical tests

Consider the following test:

0.98 What is the probability that if you choose at random one answer of
this test, your answer will turn out to be correct?

1.  2/5

2.  3/5

3.  3/5

4.  2/5

5.  3/5

As you can see, all answers above may be considered correct, but none of
them is 1!

Given the number of answers n of a test, how many such paradoxical tests
exist? Note that the order of the answers is relevant. For instance, a
test with d) 3/5 and e) 2/5 would be considered different to the one
above.

Input

Input consists of several cases, each one with a number n between 1 and
1000.

Output

For every n, print the number of paradoxical tests with n answers modulo
1006133.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T12:22:11.294Z

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