Circles

There are $N$ circles on a plane. The center of the $i$-th circle is $(x\_i, y\_i)$, and the radius of this circle is $\sqrt{x\_i^2 + y\_i^2}$.

Count the number of lattice points (points with integer coordinates) that are inside at least one of the circles. Note that the boundaries are considered to be inside.

$N$ 
$x\_1$ $y\_1$ 
$x\_2$ $y\_2$ 
$\vdots$ 
$x\_N$ $y\_N$

Print the answer in a single line.

•  $1 \leq N \leq 10^5$ 
•  $-10^5 \leq x\_i, y\_i \leq 10^5$ 
•  $(x\_i, y\_i)$ are pairwise distinct.
•  $(x\_i,y\_i) \neq (0, 0)$ 
• All values in the input are integers.