Character time vector to numeric time vector

I have the following vector:

vec <- c("01:10","12:42","1:43:02")

I would like to know how to convert it into a numeric vector counting seconds from 00:00. Does anyone have an idea on how to proceed?

Thanks

library(hms)

ifelse(is.na(parse_hms(vec)),
       parse_hm(vec),
       parse_hms(vec))
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01:10 is 4200 seconds.

3600+10*60 seconds

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Thanks for the answer. However, it only worked for "1:43:02"


vec <- c("01:10","12:42","1:43:02")

 ifelse(is.na(parse_hms(vec)),
       parse_hm(vec),
       parse_hms(vec))  parse_hms(vec))

[1]  4200 45720  6182`

I'm not sure why, but I will keep trying.
splts <- str_count(vec,":")
vec2 <- ifelse(splts==1,
               paste0("0:",vec),
               vec)

library(hms)
parse_hms(vec2) %>% as.integer()
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Sorry, I should have been more clear. "01:10" refers to 0 hours, 1 minute, and 10 seconds.