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,     1,    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

----------------------------------------------------------------------
------------------------------------------------------------
-SECURITY/CONFIDENTIALITY WARNING-

This message and any attachments are intended solely for the individual or entity to which they are addressed. This communication may contain information that is privileged, confidential, or exempt from disclosure under applicable law (e.g., personal health information, research data, financial information). Because this e-mail has been sent without encryption, individuals other than the intended recipient may be able to view the information, forward it to others or tamper with the information without the knowledge or consent of the sender. If you are not the intended recipient, or the employee or person responsible for delivering the message to the intended recipient, any dissemination, distribution or copying of the communication is strictly prohibited. If you received the communication in error, please notify the sender immediately by replying to this message and deleting the message and any accompanying files from your system. If, due to the security risks, you do not wish to receive further communications via e-mail, please reply to this message and inform the sender that you do not wish to receive further e-mail from the sender. (LCP301)