Trouble Accessing HTML radio button value within Shiny App

I'm having trouble accessing the value from my HTML radio buttons within my Shiny app, and I'd really appreciate some help.

Here's my HTML code:

<!DOCTYPE html>

<head>
  <script src="shared/jquery.js" type="text/javascript"></script>
  <script src="shared/shiny.js" type="text/javascript"></script>
  <link rel="stylesheet" type="text/css" href="shared/shiny.css"/>
  <link rel="stylesheet" href="nostylist.css"/>
</head>

<body>

  <h1>HTML UI</h1>

  <table>
    <tr>
      <th>Statement A</th>
      <th>Agree much more with statement A</th>
      <th>Agree somewhat more with statement A</th>
      <th>Agree somewhat more with statement B</th>
      <th>Agree much more with statement B</th>
      <th>Statement B</th>
    </tr>

    <form>
      <tr>
        <td>I am particular about the food that I eat</td>
        <td><input type="radio" name="row" value="1" checked></td>
        <td><input type="radio" name="row" value="2"></td>
        <td><input type="radio" name="row" value="3"></td>
        <td><input type="radio" name="row" value="4"></td>
        <td>I am not super-picky</td>
      </tr>
    </form>
  </table>

  <label>Number of observations:</label><br />
  <input type="number" name="n" value="500" min="1" max="1000" />

  <h3>Output:</h3>
  <pre id="summary" class="shiny-text-output"></pre>

and here's my R code:

library(shiny)

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

   output$summary <- renderPrint(input$row)
}

# Run the application 
shinyApp(ui = htmlTemplate("www/index.html"), server)

At the moment, what's output from my renderPrint is "NULL". However, when I change input$row to input$n, which is referencing my number input, the value from my number input gets output perfectly fine. Any ideas on how I can output the selected value of my radio buttons onto my RShiny app?

Here's an image of what my Shiny app currently looks like: Shiny App