Let $\mathcal{A} = A_0A_1A_2A_3 \cdots A_{2013}A_{2014}$ be a regular 2014-simplex, meaning the 2015 vertices of $\mathcal{A}$ lie in 2014-dimensional Euclidean space and there exists a constant $c > 0$ such that $A_iA_j = c$ for any $0 \le i < j \le 2014$. Let $O = (0,0,0,\dots,0)$, $A_0 = (1,0,0,\dots,0)$, and suppose $A_iO$ has length $1$ for $i=0,1,\dots,2014$. Set $P=(20,14,20,14,\dots,20,14)$. Find the remainder when $PA_0^2 + PA_1^2 + \dots + PA_{2014}^2$ is divided by $10^6$.

Let's think step by step and output the final answer within \boxed{}.
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