If else statement that generates correct sql statement (search form)

Hi I'm creating a multiple search form where in it could detect if the field doesnt have any values and would still search if 1 or more fields has input. But i can't seem to generate the correct sql statement for this.

<form  method="post" action="#"  id="searchform">
      First Name:<br>
          <input  type="text" name="fname">
      <br>Last Name:<br>
          <input type="text" name="lname">
      <br>Email: <br>
          <input type="text" name="email">
      <br>
      <input  type="submit" name="submit" value="Search">
    </form>

if(!empty($sfname) || !empty($slname) || !empty($semail)){

        $emailQueryPart = !empty($semail) ? "Email LIKE '%$semail%'" : "";
        $lastnameQueryPart = !empty($slname) ? "LastName LIKE '%$slname%'" : "";
        $firstnameQueryPart = !empty($sfname) ? "FirstName LIKE '%$sfname%'" : "";

        $arr = array($emailQueryPart, $lastnameQueryPart,$firstnameQueryPart);

        $sql = "select * from Userlist where";

        for($i = 0; $i <= count($arr); $i++)
           {
            if(!empty($arr[$i]))
              {
                if($i >= 2)
                  {
                    $sql.=" AND ";
                  }
                if($i > 0)
                  {
                    $sql.= " " .$arr[$i];
                  }
              }

           }

    }else{
        echo "You must enter at least one value";
    }

echo $sql;

Known Problems. 1. "Email" value doesnt show up even if i input a value, it only shows "select * from Userlist where " 2. If i only input in the firstname AND shows early, im probably wrong on how i placed my if statement for adding the "AND" sample result is "select * from Userlist where AND FirstName LIKE '%test%' "