Counting with multiple criteria using data table

I have a data.table which is shown below. I want to count combinations of
columns on i and count on j with by. A few examples are given below the
table.



I want to:

all months to show on the output including those that they have zero value

I want the three statements combined in on if possible so the output will
be one data table; that is the outputs are next to each other as manually
illustrated on the last part (desired output).





Thanks--EK

Test

Color Grade Value  Month Day

 1: yellow     A    20    May   1

 2:  green     B    25   June   2

 3:  green     A    10  April   3

 4:  black     A    17 August   3

 5:    red     C     5    May   5

 6: orange     D     0   June  13

 7: orange     E    12  April   5

 8: orange     F    11 August   8

 9: orange     F    99  April  23

10: orange     F    70    May   7

11:  black     A    77   June  11

12:  green     B    87 August  33

13:  black     A    79  April   9

14:  green     A    68    May  14

15:  black     C    90   June  31

16:  green     D    79 August  11

17:  black     E   101  April  17

18:    red     F    90   June  21

19:    red     F   112 August  13

20:    red     F   101  April  20

Test[Color=="green"&Grade=="A", .N, by=Month]

Month N

1: April 1

2:   May 1

Test[Color=="orange"&Grade=="F", .N, by=Month]

Month N

1: August 1

2:  April 1

3:    May 1

Test[Color=="orange"&Grade=="F", .N, by=Month]

Month     N

1: August     1

2:  April     1

3:    May     1

Test[Color=="red"&Grade=="F", .N, by=Month]

Month N

1:   June 1

2: August 1

3:  April 1



Desired output

                N1           N2           N3

April       1              1              1

May       1              1              1

June        0              0              0

August 0                1              1