Sequentially abnormal sequence!

Algebra Level 5

Suppose the sequence \({ a }_{ 1 }, { a }_{ 2 },..., { a }_{ 2017 }\) satisfies the following conditions:

\({ a }_{ 1 } = 0\), \(\left| { a }_{ 2 } \right| = \left| { a }_{ 1 } + 1 \right|\)\(,...,\)

\(\left| { a }_{ 2017 } \right| =\left| { a }_{ 2016 }+1 \right| \).

Find the minimum value of \(\dfrac 1{2017} \displaystyle \sum _{ r=1 }^{ 2017 }{ a }_{ r }\)

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