The number 8 is the sum and product of the numbers in the collection of four positive integers $\{1,1,2,4\}$, since $1+1+2+4=8$ and $1 \times 1 \times 2 \times 4=8$. The number 2007 can be made up from a collection of $n$ positive integers that multiply to 2007 and add to 2007 . What is the smallest value of $n$ with $n>1$ ?
(A) 1171
(B) 1337
(C) 1551
(D) 1777
(E) 1781