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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