Adding a row number respecting the order of each row

I have a table like this

id, period, tag
1     1      A
1     2      A
1     3      B
1     4      A
1     5      A
1     6      A
2     1      A
2     2      B
2     3      B
2     4      B
2     5      B
2     6      A

I would like to add a new column with a ranking, respecting the order of the row given my column ‘period’ to obtain something like this

id, period, tag  rank
1     1      A     1
1     2      A     1
1     3      B     2
1     4      A     3
1     5      A     3
1     6      A     3
2     1      A     1
2     2      B     2
2     3      B     2
2     4      B     2
2     5      B     2
2     6      A     3

What can I do?

I try rank and dense_rank function without any success

Answer

And another candidate for CONDITIONAL_CHANGE_EVENT() less code, and quite effective, too …!

WITH
input(id,period,tag) AS (
          SELECT 1,1,'A'
UNION ALL SELECT 1,2,'A'
UNION ALL SELECT 1,3,'B'
UNION ALL SELECT 1,4,'A'
UNION ALL SELECT 1,5,'A'
UNION ALL SELECT 1,6,'A'
UNION ALL SELECT 2,1,'A'
UNION ALL SELECT 2,2,'B'
UNION ALL SELECT 2,3,'B'
UNION ALL SELECT 2,4,'B'
UNION ALL SELECT 2,5,'B'
UNION ALL SELECT 2,6,'A'
)
SELECT
  *
, CONDITIONAL_CHANGE_EVENT(tag) OVER(PARTITION BY id ORDER BY period) + 1 AS rank
FROM input;
-- out  id | period | tag | rank 
-- out ----+--------+-----+------
-- out   1 |      1 | A   |    1
-- out   1 |      2 | A   |    1
-- out   1 |      3 | B   |    2
-- out   1 |      4 | A   |    3
-- out   1 |      5 | A   |    3
-- out   1 |      6 | A   |    3
-- out   2 |      1 | A   |    1
-- out   2 |      2 | B   |    2
-- out   2 |      3 | B   |    2
-- out   2 |      4 | B   |    2
-- out   2 |      5 | B   |    2
-- out   2 |      6 | A   |    3
-- out (12 rows)
-- out 
-- out Time: First fetch (12 rows): 14.823 ms. All rows formatted: 14.874 ms