sqrt log sin

Dohyun is doing his math homework. The assignment reads as follows.

Consider the sequence defined recursively by

$x_0 = 1$

$x_i = x_{\lfloor i - \sqrt{i} \rfloor} + x_{\lfloor \ln(i) \rfloor} + x_{\lfloor i \sin^2(i) \rfloor}$

Compute the value of $x_{1000000}$.

More generally, write a program that, given an integer $i$, computes $x_i$. Here $\lfloor y \rfloor$ is the floor of $y$ (the greatest integer not exceeding $y$), $\ln$ is the natural logarithm, and the argument of $\sin$ is measured in radians.

The input consists of several test cases, one integer $i$ per line, where $0 \le i \le 10^6$.

The last line contains $-1$, which marks the end of the input and must not be processed.

For each given $i$, print $x_i$ modulo $10^6$ on its own line.