There are at least 3 way of thinking, to answer to this problem.

- Derive a function
*f*(*x*) such that*n*=*f*(*n*-1), using only the set of keys. - Derive an integer
*m*(*m*>*n*) then decrease the number toward*n*using a function*h*(*x*) such that*m*=*h*(*m*+1). - Derive the way such that