A dog is standing at the bottom left corner of a grid of \(46 \times 46\) streets. The dog is trying to get to the top right corner of the grid, where it knows there is some food. As the dog runs, between the corners, it will only ever run up and to the right. Any time the dog runs to the right, it runs at least \(4\) consecutive blocks to the right, and any time it runs up, it runs at least \(12\) consecutive blocks up. How many different intersections are unreachable for the dog by following these rules?
Details and assumptions
The last stretch that the dog runs must also satisfy the condition on the minimum number of consecutive blocks.
An intersection is reachable if the dog runs through it. It doesn't matter if the dog can change direction at that intersection. Remember that the dog needs to exit through the top right corner of the grid.