Aggressive rooks P94143

Consider a chessboard with $n$ rows and $n$ columns. In how many ways can we place $n$ rooks so that at least two rooks threaten each other?

For instance, these are two of the ways for $n = 6$:

Input

Input consists of several numbers $1\leq n\leq 6$. A special case with $n = 0$ marks the end of input.

Output

For every $n$, print the number of different ways to place $n$ rooks on a chessboard $n \times n$ so that at least two rooks threaten each other. For every $1\leq n\leq 6$, this number has less than 10 digits.