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Let $r=(r_0,r_1,...,r_n)$ denote the set of radii of each circle (corresponding either to $2$, $4$, $7$, or $9$ cells); let $s$ denote the distance from the center of one circle to the center of another.  In this application, Generally,  a random walk of length $N$ in a 100✕100 $2$-dimensional integer lattice ${\Bbb Z}^2$ (also known as a square lattice), starting at point $x$, is defined as a path \begin{equation}  ω=(ω_0, ω_1, ..., ω_n)  \end{equation}  Here In this case  $ω_b ∈ {\Bbb Z}^2$, $ω_0=x$, $|ω_b−ω_{b−1}| = 1$, where $b = 1, 2, . . . , n$, and $r_c+r_d \neq \geq  s$, and $0≤c