# Tricky, tricky

In a certain game, the first player secretly chooses an $$2015-$$dimensional vector $$a = (a_1, a_2, . . . , a_{2015})$$ all of whose components are integers.

The second player is to determine $$a$$ by choosing any $$2015-$$dimensional vectors $$x_i$$, all of whose components are also integers.

For each $$x_i$$ chosen, and before the next $$x_i$$ is chosen, the first player tells the second player the value of the dot product $$x_i \cdot a$$.

What is the least number of vectors $$x_i$$ the second player has to choose in order to be able to determine $$a$$?

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