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?

$2/5$
$3/5$
$3/5$
$2/5$
$3/5$

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