Add dynamic row rank to shiny DT

Question

I am trying to add a row rank from smallest value to largest value in my shiny Data Table based on the order of the rows. I want the row rank to update based on the column that is ordered. My best ideas would either be to use rownames but those change with the rows or to use input$table_state$order and saveState to figure out what column is being ordered and then recalculate a rank column. I've included an example using the iris dataset.

library(shiny)
library(DT)
library(tidyverse)

data = iris %>% distinct(Species, .keep_all = TRUE) %>%
    arrange(Sepal.Length) %>%
    mutate(rank = 1:3) %>%
    select(rank, Species, everything())


# Define UI for application that draws a histogram
ui <- fluidPage(
 DT::dataTableOutput("table")
)


# Define server logic required to draw a histogram
server <- function(input, output) {

output$table = DT::renderDataTable({
DT::datatable(data,
              rownames = FALSE,
              options = list(
                columnDefs = list(list(orderable = FALSE, targets = 0:1)),
                order = list(list(2, "asc")),
                ordering = TRUE
              ))
})

}

# Run the application 
shinyApp(ui = ui, server = server)