## SKYLINE - Skyline

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The director of a new movie needs to create a scaled set for the movie. In the set there will be N skyscrapers, with distinct integer heights from 1 to N meters. The skyline will be determined by the sequence of the heights of the skyscrapers from left to right. It will be a permutation of the integers from 1 to N.

The director is extremely meticulous, so she wants to avoid a certain sloping pattern. She doesn’t want for there to be ANY three buildings in positions i, j and k, i < j < k, where the height of building i is smaller than that of building j, and building j’s height is smaller than building k’s height.

Your task is to tell the director, for a given number of buildings, how many distinct orderings for the skyline avoid the sloping pattern she doesn't like.

### Input

There will be several test cases in the input. Each test case will consist of a single line containing a single integer N (3 ≤ N ≤ 1,000), which represents the number of skyscrapers. The heights of the skyscrapers are assumed to be 1, 2, 3, ..., N. The input will end with a line with a single 0.

### Output

For each test case, output a single integer, representing the number of good skylines - those avoid the sloping pattern that the director dislikes - modulo 1,000,000. Print each integer on its own line with no spaces. Do not print any blank lines between answers.

### Example

`Input:340Output:514`