Complex yet real?

We call the complexity of an integer nn as the least number of 1s required to build the integer nn using only additions, multiplications and parentheses.

Let C(n)\mathcal C (n) denote the complexity of the integer nn. Find the value of C(2016)\mathcal C(2016) .

Details and Assumptions

As an explicit example, the least number of 1s required to build the integer 6 is 5 because 6=(1+1)×(1+1+1)6 = (1+1)\times(1+1+1) and we cannot build the integer 6 with four 1's or less.

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