2016 Digital Root

For each number nn, we define the Digital Root of nn in the following manner: Take the sum of the digits to obtain a new number. Repeat this process until the result is a single digit.

Find the digital root of 201620162016 times\underset { 2016\text{ times} }{ \underbrace { 2016\ldots2016 } } .

As an explicit example, for n=3487n=3487, 34873+4+8+7=222+2=4  .3487\quad \rightarrow \quad 3+4+8+7=22\quad \rightarrow \quad 2+2=4 \; . Therefore, the digital root of 3487 is 4.

Clarification: In the number above, 2016 appears 2016 times in its decimal representation.

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