Replace missing values if previous and next values are consistent

Question

I am currently working with time series data which looks something like the following:

ID	Var1	Var2	Var3	Var4	Var5
1	A	NA	A	NA	A
2	B	C	NA	NA	B
3	A	A	NA	NA	A
4	A	B	NA	NA	B
5	C	NA	B	NA	B

df <- data.frame("ID" = c(1, 2, 3, 4, 5),
             "Var1" = c("A", "B", "A", "A", "C"),
             "Var2" = c(NA, "C", "A", "B", NA),
             "Var3" = c("A", NA, NA, NA, "B"),
             "Var4" = c(NA, NA, NA, NA, NA),
             "Var5" = c("A", "B", "A", "B", "B"))

I wish to fill in the "NA" values if the first non-missing previous and first non-missing next value are consistent. That is, the desired result would be

ID	Var1	Var2	Var3	Var4	Var5
1	A	A	A	A	A
2	B	C	NA	NA	B
3	A	A	A	A	A
4	A	B	B	B	B
5	C	NA	B	B	B

Where the data for ID = 2 is not replaced, since Var2 and Var5 do not match. Moreover, the missing value for ID = 2 at Var2 is not replaced, since Var1 and Var3 are not consistent. I am struggling with how to accomplish this, and any help would be appreciated.