Count based on multiple conditions using sqldf

Hi all I'm writing a sql query on R using sqldf and seem to hit a roadblock. I have a table with an Id column, two dates columns and a grouping by column.

AlertDate  AppointmentDate  ID  Branch
01/01/20   04/01/20         1   W1
01/01/20   09/01/20         1   W1
08/01/20   09/01/20         1   W2
01/01/20   23/01/20         1   W1

The query I'm writing is

sqldf('select Branch,count(ID) from df where AlertDate <= AppointmentDate 
and AppointmentDate <AlertDate+7 group by Branch')

From this query the result I'm getting is

Branch Count
W1      1
W2      1

Whichis correct based on the query. What I want to achieve is if my 2nd condition is false ie AppointmentDate is less than AlertDate+7. Instead of dropping the count it should be counted in the next group depending on date. Example if the alertdate is 01/01/20 and appointment date is 23/01/20 then it should be counted in W4. ceil((Appointmentdate-alertdate)/7) SO in the end I want the result as

Branch  Count
W1      1
W2      2
W4      1

The second row should be counted in W2 and 4th should be in W4 rather than being discarded. I was trying to achieve this in sql using sqldf in R. Any possible solution using R or Sql would work for me.

Output of dput(test)

structure(list(AlertDate = structure(c(18262, 18262, 18269), class = "Date"), 
AppointmentDate = structure(c(18265, 18270, 18270), class = "Date"), 
ID = c(1, 1, 1), Branch = c("W1", "W1", "W2")), class = c("spec_tbl_df","tbl_df", "tbl", "data.frame"), row.names = c(NA, -3L), problems = structure(list(
row = 3L, col = "Branch", expected = "", actual = "embedded null", 
file = "'C:/Users/FRssarin/Desktop/test.txt'"), row.names = c(NA,-1L),
 class = c("tbl_df", "tbl", "data.frame")), spec = structure(list(
cols = list(AlertDate = structure(list(format = "%d/%m/%y"), class = c("collector_date","collector")), AppointmentDate = structure(list(format = "%d/%m/%y"), class = c("collector_date","collector")), ID = structure(list(), class = c("collector_double", "collector")), Branch = structure(list(), class = c("collector_character", "collector"))), default = structure(list(), class = c("collector_guess", "collector")), skip = 1), class = "col_spec"))