.htaccess url重写规则将非现有页面重定向到它不应该的页面

I have an URL Rewrite rule in .thaccess that does exactly what I want it to:

RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^([^/]+)$ /page.php?id=$1 [L]

So requests to www.site.com/page.php?id=one are redirected to this: www.site.com/one, which is what is needed.

However, there is a problem - if any of the other filenames in the main dir is misspelled then the browser redirects to www.site.com/page.php?id=

So for example if the name of www.site.com/other.php is misspelled with anything like www.site.com/otherr.php, then the .htaccess rule kicks in and the URL the user sees is www.site.com/otherr.php, while the content showing is the one of page.php.

Any ideas what in the rewrite rule needs to be changed to remediate this problem?