How rewriting for directory in root directory

I want to change my url. Here I have a directory structure like this

htdocs/
      example/
              public/
                     login.php
                     people/
                            people1.php
                            people2.php
                     animal/
                            animal1.php
                            animal2.php
                     404.php
              assets/
                    css/
                    js/

then I want the url like below in accordance with the existing directory in the root

localhost/example/login
localhost/example/people/people1
localhost/example/people/people2
localhost/example/animal/animal1
localhost/example/animal/animal2

I've tried making an .htaccess file with the following contents

Options +FollowSymLinks
RewriteEngine On
rewritecond %{REQUEST_URI} !^/public/(.*)
rewritecond %{REQUEST_URI} !^/assets/(.*)
RewriteRule .* index.php [L]

and it's index.php

$requested = empty($_SERVER['REQUEST_URI']) ? false : $_SERVER['REQUEST_URI'];

switch ( $requested ) {

    case '/login':
        include 'public/login.php';
        break;
    default:
        include 'public/404.php';
}

when I headed localhost/example/login, but destination is 404.php (ERROR).

can you help me?