# Complex yet real?

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

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

Details and Assumptions

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

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