In Pandas DataFrame how can I increment the values per row if it matches a character

Question

This is somewhat similar to this question but a little bit complex.

Assuming I have this table:

data = {'column1': ['A1', 'A1', 'A1', 'A1'],
        'column2': ['A9', 'A1', 'A8', 'A1'],
        'column3': ['D1', 'D1', 'D1', 'D1'],
        'column4': ['A6', 'A2', 'A3', 'A4'],
        'column5': ['H1', 'H1', 'H1', 'H1'],
        'column6': ['A4', '', '', 'A3'],
        'column7': ['A5', '', '', 'A9']}

df = pd.DataFrame(data)

+---------+---------+---------+---------+---------+---------+---------+
| column1 | column2 | column3 | column4 | column5 | column6 | column7 |
+---------+---------+---------+---------+---------+---------+---------+
| A1      | A9      | D1      | A6      | H1      | A4      |  A5     |
| A1      | A1      | D1      | A2      | H1      |         |         |
| A1      | A8      | D1      | A3      | H1      |         |         |
| A1      | A1      | D1      | A4      | H1      | A3      |  A9     |
+---------+---------+---------+---------+---------+---------+---------+

my goal here is to reset the number counterpart of all values containing "A" per row, starting with A1. if "A1" re-occurs on the same row, move to the next cell. Also, values that is not "A" and blanks should be ignored.

+---------+---------+---------+---------+---------+---------+---------+
| column1 | column2 | column3 | column4 | column5 | column6 | column7 |
+---------+---------+---------+---------+---------+---------+---------+
| A1      | A2      | D1      | A3      | H1      | A4      | A5      |
| A1      | A1      | D1      | A2      | H1      |         |         |
| A1      | A2      | D1      | A3      | H1      |         |         |
| A1      | A1      | D1      | A2      | H1      | A3      | A4      |
+---------+---------+---------+---------+---------+---------+---------+