Remove one "folder" from URL with a 301 redirect, keep both URLs working

My site URL: http://example.com/website/pages/home

Wanted URL: http://example.com/pages/home

I need this to be a 301 redirect so that search engines update my links.

This is what I got so far:

Options +FollowSymLinks
Options -Indexes
DirectoryIndex index.php index.html
RewriteEngine on
\# remove /website/
RedirectMatch  ^(.+)(/website/)(.+)$ $1/$3 [L]
\# remove index.php from URL
RewriteCond $1 !^(index\.php^)
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php/$1 [L,QSA]
\# deny access to wget user agent
RewriteCond %{HTTP_USER_AGENT} wget [NC]
RewriteRule 开发者_如何学JAVA(.*) /$1 [L]

What happens with this rules:

Inserted URL: http://example.com/website/pages/home

Redirected URL: http://example.com/index.php/pages/home

Expected results: http://example.com/pages/home

Thanks in advance for your help.

**SOLVED**

Options +FollowSymLinks
Options -Indexes
DirectoryIndex index.php index.html

RewriteEngine on

# remove /website/
RedirectMatch  ^(.+)(index.php/website/)(.+)$ $1$3 [R=301,L]

# remove index.php from URL
RewriteCond $1 !^(index\.php^)
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php/$1 [L,QSA]

# deny access to wget user agent
RewriteCond %{HTTP_USER_AGENT} wget [NC]
RewriteRule (.*) /$1 [L]

---

RewriteRule ^(.*)$ index.php/$1 [L,QSA]

what if you remove index.php from this line? I think this line inserts index.php into your URL.