Removing Trailing Slash from URL in Nginx

I would like the following URLs on my site to be equivalent:

/foo/bar
/foo/bar/
/foo/bar/index.html

and further I would like the second two forms to issue HTTP 301 redirects to the first form. I am just serving static pages, and they are arranged according to the third form. (In other words, when a user requests /foo/bar they should receive the file at /usr/share/.../foo/bar/index.html).

My nginx.conf currently contains the following:

rewrite ^(.+)/$ $1 permanent;
index index.html;
try_files $uri $uri/index.html =404;

This works for requests for /foo/bar/index.html, but when I request /foo/bar or /foo/bar/ Safari tells me that “too many redirects occurred”—I assume there’s an infinite redirect loop or something like that. How can I get nginx to map URLs to files in the way I’ve described?

Edit: My full configuration

Here is my entire nginx.conf with my domain name replaced with “example.com”.

user www-data;
worker_processes 1;
pid /run/nginx.pid;

events {
  worker_connections 768;
}

http {
  sendfile on;
  tcp_nopush on;
  tcp_nodelay on;
  keepalive_timeout 65;
  types_hash_max_size 2048;
  server_tokens off;

  server_names_hash_bucket_size 64;

  include /etc/nginx/mime.types;
  default_type application/octet-stream;

  access_log /var/log/nginx/access.log;
  error_log /var/log/nginx/error.log;

  gzip on;
  gzip_disable "msie6";
  gzip_vary on;
  gzip_proxied any;
  gzip_comp_level 6;
  gzip_buffers 16 8k;
  gzip_http_version 1.1;
  gzip_types text/plain text/css application/json application/x-javascript text/xml application/xml application/xml+rss application/atom+xml text/javascript image/svg+xml;

  server {
    server_name www.example.com;
    listen 80;
    return 301 $scheme://example.com$request_uri;
  }

  server {
    server_name example.com 123.45.67.89 localhost;
    listen 80 default_server;

    # Redirect /foobar/ to /foobar
    rewrite ^(.+)/$ $1 permanent;

    root /usr/share/nginx/www/example.com;
    index index.html;
    try_files $uri $uri/index.html =404;

    error_page 404 /404.html;
    error_page 500 502 503 504 /50x.html;

    location = /50x.html {
      root /usr/share/nginx/html;
    }
  }
}