#### 1994-1995 ACM International Collegiate Programming Contest

Western
European Regional

Practice Session

# Problem E

## Rooks

Most people participating in the ACM scholastic
programming contest have at some stage been asked: 'Can you give an example of
the type of problems you have to solve there?'. The most common example selected
in response is the 8-queens problem.
Of course, all of you have at one time or the other programmed the 8-queens
problem. So here is a small variation on that theme: determine the number of
ways you can place *R* rooks on an *R* × *R* chess board,
such that no two rooks are on the same file or on the same rank.

### Input Specification

The first line of input contains an integer
*N*, specifying the number of test cases. Each of the *N* test
cases consists of a single positive integer *R* (1 <= *R* <=
12) on a line by itself, indicating which *R*-rooks problem you have to
solve.
### Output Specification

For each test case, output the line '```
There
are
```*S* solutions to the *R*-rooks problem.

', where
*S* is the number of solutions, and *R* is the size of the
problem.
### Example Input

3
1
2
4

### Example Output

There are 1 solutions to the 1-rooks problem.
There are 2 solutions to the 2-rooks problem.
There are 24 solutions to the 4-rooks problem.