Calculate without substitution 1 + a + 2b + 3c + 2ab + 3ac + 6bc + 6abc if a=999, b=666 and c=333

Question

If
abcde=1 (where a,b,c,d and e are all positive real numbers)
then
what is the minimum value of a+b+c+d+e?

Answer 1

Factors are
(1+a)(1+2b)(1+3c)
=> (1+999)(1+2*666)(1+3*333)
=> 1000*1333*1000
=> **************

Answer: **********