Need to separate strings into multiple variables based on numeric versus non-numeric

I have a data frame with one variable. It looks something like this:

df <- data.frame(c("25 Edgemont 52 Sioux County", "57 Burke 88 Papillion-LaVista South"))

To provide more context, each observation/row is a basketball game score. I would like to separate into four data frame columns that splits the numbers and team names up. So for example, the first row would end up as "25" in first column, "Edgemont" in second column, "52" in third column, and Sioux City in fourth column.

I've tried the below and various SO suggestions but can't get the desired results:

df2 <- strsplit(gsub("([0-9]*)([a-z]*)([0-9]*)([a-z]*)", "\\1 \\2 \\3 \\4", df), "")