Pandas: counting all combinations of values in multiple columns

The following is an example of items rated by 1,2 or 3 stars. I am trying to count all combinations of items per month and ratings (stars).

In the following example, item 10 was rated in month 1 and has two ratings equal 1, one rating equal 2 and one rating equal 3.

inp = pd.DataFrame({'month':[1,1,1,1,1,2,2,2], 
                    'item':[10,10,10,10,20,20,20,20], 
                    'star':[1,2,1,3,3,2,2,3]}
                  )

 month item star
0   1   10  1
1   1   10  2
2   1   10  1
3   1   10  3
4   1   20  3
5   2   20  2
6   2   20  2
7   2   20  3

For the given above input frame output should be:

   month    item    star_1_cnt  star_2_cnt  star_3_cnt
0   1       10      2           1           1
1   1       20      0           0           1
2   2       20      0           2           1

I am trying to solve the problem starting with the following code, which result still needs to be converted to the desired format of the output frame and which gives the wrong answers:

1   20  3   (1, 1)
2   20  3   (1, 1)

Anyway, there should be a better way to create the output table, then finalizing this one:

months = [1,2]
items = [10,20]
stars = [1,2,3]

d = {'month': [], 'item': [], 'star': [], 'star_cnts': [] }

for month in months:
    for star in stars:
        for item in items:
            star_cnts=dict(inp[(inp['item']==item) & (inp['star']==star)].value_counts()).values()
            d['month'].append(month)
            d['item'].append(item)
            d['star'].append(star)
            d['star_cnts'].append(star_cnts)
            
pd.DataFrame(d)

    month   item    star    star_cnts
0   1       10      1       (2)
1   1       20      1       ()
2   1       10      2       (1)
3   1       20      2       (2)
4   1       10      3       (1)
5   1       20      3       (1, 1)
6   2       10      1       (2)
7   2       20      1       ()
8   2       10      2       (1)
9   2       20      2       (2)
10  2       10      3       (1)
11  2       20      3       (1, 1)

​

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