The function F(x) is defined for all positive real values of x and is such that:

F(3x) = 3F(x), and:
F(x) = 1 - abs(x-2) for 1 ≤ x ≤ 3.

Determine the minimum value of x for which F(x) = F(2001).

*** abs(x) refers to the absolute value of x.