In my website I have all the links are relative and look like var1/ or var1/var2/

I want to redirect them to index.php?p=var1 or index.php?p=var1/var2 without changing the address in the address bar. So I did this:

RewriteEngine on
RewriteRule ^(.+)/$ index.php?p=$1 [QSA,L]

and it works fine.
But I'd also like to send relative links like var1 and var1/var2 to the same index.php?p=var1 and index.php?p=var1/var2, so I modified the .htaccess like this:

RewriteEngine on
RewriteCond %{SCRIPT_FILENAME}!^index\.php$
RewriteCond %{SCRIPT_FILENAME}!^.+/$
RewriteRule ^(.+)$ $1/ [are=301]
RewriteRule ^(.+)/$ index.php?p=$1 [QSA,L]

obviously it doesn't work as I hoped... but why?

Thanks!