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@media(max-width:767px) {
    .navbar .navbar-form {
        width: 185px;
        padding-left:0;
        padding-right:0;
    }
}
@media(min-width:768px) {
    .navbar .navbar-form {
        width: 250px;
    }
}
.navbar .navbar-form {
    padding-top: 0;
    padding-bottom: 0;
    margin-right: 0;
    margin-left: 0;
    border: 0;
    -webkit-box-shadow: none;
    box-shadow: none;
}

<div class="navbar navbar-inverse navbar-fixed-top">
   <div class="container">
      <div class="navbar-header">
         <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">
         <span class="icon-bar"></span>
         <span class="icon-bar"></span>
         <span class="icon-bar"></span>
         </button>
         <a class="navbar-brand hidden-xs" href="#">CompAny</a>
         <a class="navbar-brand visible-xs" href="#">C</a>
         <form class="navbar-form pull-left" role="search">
            <div class="input-group">
               <input type="text" class="form-control" placeholder="Search">
               <div class="input-group-btn">
                  <button type="submit" class="btn btn-default"><span class="glyphicon glyphicon-search"></span></button>
               </div>
            </div>
         </form>
      </div>
      <div class="navbar-collapse collapse">
         <ul class="nav navbar-nav navbar-right">
            <li class="active"><a href="#">Home</a></li>
            <li><a href="#about">Browse Courses</a></li>
            <li><a href="#contact">Active Courses</a></li>
         </ul>
      </div>
      <!--/.navbar-collapse -->
   </div>
</div>