.htaccess redirect 301 using rewrite rule - apache

Question

I'm trying to beautify some urls. I configured the htaccess file so my urls are changed:
old url: http://mysite.com/index.php?id=45tye4
new url: http://mysite.com/45tye4
I want now to permanently redirect old urls to new urls. This is what I try with no luck:
RewriteRule ^index.php?id=(.*)$ $1 [R=301,L]
The main problem seems to be the '?' in the url. When I try the same url without ? the redirect works. I also tried other variants with no luck:
RewriteRule ^index.php\?id=(.*)$ $1 [R=301,L]
RewriteRule ^index.php[\?]id=(.*)$ $1 [R=301,L]
Update:
I added the redirection according to anubhava instructions. The redirection works, but unfortunately I get into a redirect loop. I thought [L] flag should solve the redirection loop, but it doesn't.
RewriteCond %{QUERY_STRING} ^id=(.*)$
RewriteRule ^index\.php/?$ /%1? [R=301,L]
RewriteRule ^(.*)$ index.php?id=$1 [L]

Answer 1

RewriteRule matches only REQUEST_URI. You have to use RewriteCond to match Query string
Try this code:
Options +FollowSymlinks -MultiViews
RewriteEngine on
RewriteCond %{THE_REQUEST} ^GET\s/+index\.php [NC]
RewriteCond %{QUERY_STRING} (^|&|\?)id=(.*)(&|$) [NC]
RewriteRule . /%2? [R=301,L,NC]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^(.+)$ index.php?id=$1 [L]
This will redirect old URI of /index.php?id=45tye4 to new URI: /45tye4