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There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can participate in the path only once. What is the relation and the path it induces?

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The path is follows

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And the relationship is

Two numbers on the path are adjacent if and only if they are both even.
The path is unique under this requirement.

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