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Field Calculator: Referencing Field Values of Other Features (i.e. Rows)

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I have an attribute similar to the below:

FID Value
0 60
1 55
2 50
3 100
4 55
5 50
6 40
...

I'd like to add a field, and set that field equal to the maximum of the current row, or the row above/below. For example:

FID Value Local_Max
0 60 60
1 55 60
2 50 100
3 100 100
4 55 100
5 50 55
6 40 ...
...

I assume there's no way to do this without code? Thanks for the help

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