\mathrm{p}_{ij} = \left\{ \begin{array}{ll} i^2/N^2 & j=i-1 \\ 2i(N-i)/N^2 & j=i \\ (N-i)^2/N^2 & j=i 1 \\ 0 & \mathrm{otherwise} \end{array} \right.
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