Limit number of lines in textarea and Display line count using jQuery

Using jQuery I would like to:

• Limit the number of lines a user can enter in a textarea to a set number
• Have a line counter appear that updates number of lines as lines are entered
• Return key or \n would count as line

$(document).ready(function(){
  $('#countMe').keydown(function(event) {
    // If number of lines is > X (specified by me) return false
    // Count number of lines/update as user enters them turn red if over limit.

  });   
});


<form class="lineCount">
  <textarea id="countMe" cols="30" rows="5"></textarea><br>
  <input type="submit" value="Test Me">
</form>

<div class="theCount">Lines used = X (updates as lines entered)<div>

For this example lets say limit the number of lines allowed to 10.