add a variable a data frame to sequentially count unique rows

Hi R users,

In this test file,
test  <- data.frame(group1=c("g1", "g1", "g1", "g2", "g2", "g2", "g2", "g2", "g2"),
                                        group2=c("k1", "a2", "a2", "c5", "n6", "n6", "n6", "m10","m10"),
                                          count=   c( 1,       2,        2,       1,      2,   2,     2,    3,    3 ));

I have group 1 and group2 variable and want to add the count variable to sequentially count unique rows defined by group1 and group2.

I hope to use the following functions in library (tidyverse),  No one worked well.
test %>% group_by(group1, group2) %>% mutate(count = row_number()) 
test %>% group_by(group1, group2) %>% mutate(count = 1:n()) test %>% 
group_by(group1, group2) %>% mutate(count = seq_len(n())) test %>% 
group_by(group1, group2) %>% mutate(count = seq_along(group1, group2))

Can you help me to make the third column in the test data frame?

Thank you,

Ding

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