Bootstrap 3 login form with 2 input-groups in navbar - twitter-bootstrap-3

Question

I am trying to place a login form in a Bootstrap 3 navbar. I am trying to make the username and password input boxes into input groups. I know a similar question has been asked and answered here before, but none of the solutions work because I need two input groups in a single form.
This is what I have so far:
<div class="navbar navbar-default navbar-static-top" role="navigation">
<div class="container-fluid">
<div class="navbar-header">
<button class="navbar-toggle" data-target="#navbar-collapse" data-toggle="collapse" type="button">
<span class="sr-only">Toggle Navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button><a class="navbar-brand" href="/">My Site</a>
</div>
<div class="collapse navbar-collapse" id="navbar-collapse">
<form action="/login" class="navbar-form navbar-right" method="post" role="form">
<div class="form-group">
<div class="input-group">
<span class="input-group-addon">
<i class="glyphicon glyphicon-user"></i>
</span>
<input class="form-control" name="andrew_id" placeholder="Andrew ID" type="text" />
</div>
</div>
<div class="form-group">
<div class="input-group">
<span class="input-group-addon">
<i class="glyphicon glyphicon-lock"></i>
</span>
<input class="form-control" name="secret" placeholder="Secret Words" type="password" />
</div>
</div>
<button class="btn btn-primary" type="submit">Log In</button>
</form>
</div>
</div>
</div>
Also in a JSFiddle: http://jsfiddle.net/x6hk4/
Pretty much the two inputs and the button should be right aligned and be inline with the rest of the navbar.

Answer 1

This needs some work still, but perhaps it will put you in the right direction:
http://jsfiddle.net/technotarek/5rGFX/
<div class="container">
<nav class="navbar navbar-inverse navbar-default">
<div class="col-sm-3">
<a class="navbar-brand">Brand</a>
</div>
<form class="navbar-form">
<div class="col-sm-3 col-sm-offset-2">
<div class="input-group">
<span class="input-group-addon">#</span>
<input type="text" class="form-control">
</div>
</div>
<div class="col-sm-3">
<div class="input-group">
<span class="input-group-addon">#</span>
<input type="text" class="form-control">
</div>
</div>
<div class="col-sm-1">
<button class="btn btn-primary btn-block" type="button">GO</button>
</div>
</form>
</nav>
</div>
It's loosely based off of my responses to Two rows in a navbar with a column spanning two rows