______________________________________
/ Your reasoning is excellent -- it's  \
| only your basic assumptions that are |
\ wrong.                               /
 --------------------------------------
    \
     \
                                   .::!!!!!!!:.
  .!!!!!:.                        .:!!!!!!!!!!!!
  ~~~~!!!!!!.                 .:!!!!!!!!!UWWW$$$ 
      :$$NWX!!:           .:!!!!!!XUWW$$$$$$$$$P 
      $$$$$##WX!:      .<!!!!UW$$$$"  $$$$$$$$# 
      $$$$$  $$$UX   :!!UW$$$$$$$$$   4$$$$$* 
      ^$$$B  $$$$\     $$$$$$$$$$$$   d$$R" 
        "*$bd$$$$      '*$$$$$$$$$$$o+#" 
             """"          """""""