There is a highly organized city that has decided to assign a number to each of their departments:

   police department
   sanitation department
   fire department 


Each department can have a number between   1   and   7   (inclusive).

The three department numbers are to be unique (different from each other) and must add up to   12.

The Chief of the Police doesn't like odd numbers and wants to have an even number for his department.



Task

Write a computer program which outputs all valid combinations.



Possible output   (for the 1st and 14th solutions):

 --police--  --sanitation--  --fire-- 
     2             3            7 
     6             5            1



BEGIN
    # show possible department number allocations for police, sanitation and fire departments #
    # the police department number must be even, all department numbers in the range 1 .. 7   #
    # the sum of the department numbers must be 12                                            #
    INT max department number =  7;
    INT department sum        = 12;
    print( ( "police sanitation fire", newline ) );
    FOR police FROM 2 BY 2 TO max department number DO
        FOR sanitation TO max department number DO
            IF sanitation /= police THEN
                INT fire = ( department sum - police ) - sanitation;
                IF  fire > 0 AND fire <= max department number
                AND fire /= sanitation
                AND fire /= police
                THEN
                    print( ( whole( police,      -6 )
                           , whole( sanitation, -11 )
                           , whole( fire,        -5 )
                           , newline
                           )
                         )
                FI
            FI
        OD
    OD
END