Find Max value from multiple shapefiles

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I have some shapefiles lets assume I have two shapefiles , in shapefiles there are multiple polygons with some values also both shape file is from same location . two polyogons from different shapefile can have different value but they can overlap. I in between those two polygons I want to find max value in it. also I don't want to lose value where I doesn't over lap as it can overlap with something else as well. I want to do this with all polygons using R code. how can I do it?

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