How to join data tables in R (inner,outer,left,right)?

This is a replication of a previous post ( href="https://stackoverflow.com/questions/1299871/how-to-join-data-frames-in-r-inner-outer-left-right">How
to join (merge) data frames (inner, outer, left, right)?), using
data.table() rather than data.frame().

Suppose I have two data tables:

library(data.table)
dt1
            = data.table(CustomerID=c(1:6),Product=c(rep("Toaster",3),rep("Radio",3)))
dt2
            = data.table(CustomerID=c(2,4,6),State=c(rep("Alabama",2),rep("Ohio",1)))
            

dt1

 CustomerID Product
1: 1
            Toaster
2: 2 Toaster
3: 3 Toaster
4: 4 Radio
5:
            5 Radio
6: 6 Radio
dt2
 CustomerID State
1: 2
            Alabama

2: 4 Alabama
3: 6
            Ohio

setkey(dt1,CustomerID)
setkey(dt2, CustomerID)
            

The default using
merge() on a data.table is a right
join. What's the syntax for the others?

#Outer
            join:


#Right outer (data.table default): 
dtro
            <- merge(dt1,dt2); dtro 

 CustomerID Product State
1:
            2 Toaster Alabama
2: 4 Radio Alabama
3: 6 Radio
            Ohio

#Left outer:


#Cross join: