How to addPolyline of max distance, based on attributes filter from dropdown list using haversine calculation in shiny leaflet map?

Question

I am trying to show maximum distance covered from swimming events for each person in leaflet map with "shinyapp" based on filtering a "Name" and a "SwimType".

Here is my code:

library(shiny)
library(dplyr)
library(shinydashboard)
library(leaflet)
library(osrm)


swimd <- read.csv('swim.csv', stringsAsFactors = F)

ui <- shinyUI(dashboardPage(
  dashboardHeader(title = "Training"),
  dashboardSidebar("A swim session"),
  dashboardBody(
    fluidPage(
      box("", 
          leafletOutput("abc", height = 430),
          width = 8, height = 450, background = 'black'),
      box("", 
          selectInput('st', label = 'Swim Type:', choices = unique(swimd$SwimStyle)),
          selectInput('pn', label = 'Name:', choices = unique(swimd$Name)),
      
          width = 4, height = 450, background = 'black')
  
    )
  )
))

server <- shinyServer(function(input, output, session){

  a <- reactive({
    swimd %>%
      select(Name, SwimStyle, Longitude, Latitude) %>%
      filter( SwimStyle %in% input$st)
  })

  observe({
    updateSelectInput(session, 
                  inputId='pn', 
                  choices = c("< select Name>"="", a()$Name ))
  })

  output$abc <- renderLeaflet({
    leaflet() %>%
      addProviderTiles(providers$OpenStreetMap) %>%
      setView(lng=0, lat=0, zoom = 2)
  })

  observe({
    selection <- a() %>% filter(Name %in% input$pn)
    selection$res <- distHaversine(selection$Longitude, selection$Latitude, r=6378137)
    #to find the difference between two sequence values
    selection[ , list(Name, SwimStyle, Longitude, Latitude,res,Diff=diff(res))]
    b <- selection %>% arrange(desc(Diff)) %>% top_n(2)

    leafletProxy("abc") %>%  clearMarkers() %>% addMarkers(lat = b$Latitude, lng = b$Longitude) %>% 
      addPolylines(route$lon,route$lat, 
                   label = paste(round(route_summary[1]), 'Minutes  - ', round(route_summary[2]/1000), 'Meters'), 
                   labelOptions = labelOptions(noHide = TRUE))
      flyTo(lat = b$Latitude, lng = b$Longitude, zoom = 2)
  })   
})

shinyApp(ui,server)

In this app when the name and swim type filtered the maximum distance of swimming should be shown in map with 'polyline'. For an example a person finished 10 mins of swimming. For each 1 min of swimming we record the distance. I would like to show addPolyline for maximum distance covered in a min for each person by selecting a name from the dropdown list as created in this app.

Can someone help me on this use-case?

Thank you.