Let f(x)=|2\{x\}-1| where \{x\} denotes the fractional part of x. The number n is the smallest positive integer such that the equation
n f(x f(x))=x
has at least 2012 real solutions x. What is n ?
Note: the fractional part of x is a real number y=\{x\}, such that 0 \leq y<1 and x-y is an integer.
Answer Choices
A. 30
B. 31
C. 32
D. 62
E. 64