PAMO 2015 Problem 3

Let $a_1,a_2,...,a_{11}$ be integers. Prove that there are numbers $b_1,b_2,...,b_{11}$ , each $b_i$ equal $-1,0$ or $1$ , but not all being $0$ , such that the number $$N=a_1b_1+a_2b_2+...+a_{11}b_{11}$$ is divisible by $2015$ .