Number of Terms in Expansion of Polynomial

Let

$\begin{aligned}P(x)&=\displaystyle\prod_{n=1}^{10}\left(x^{2^n}-x^{2^{n-1}}+1\right)\\&=(x^2-x+1)(x^4-x^2+1)\ldots(x^{1024}-x^{512}+1).\end{aligned}$

Let $N$ be the number of terms with non-zero coefficients when $P(x)$ is expanded (including the constant term). What is the remainder when $N$ is divided by $1000$ ?