SSH tunnel: local => gateway => MySQL server

Question

I need to access a MySQL database on a remote server at my lab. The server is only accessible once I log in to a gateway server on the remote network:

local server => gateway server => MySQL server.

I can ssh to the gateway using port 24222.

I am using the PERL DBI module. This is what I use to connect when I am at the lab:

my $host="1.2.3.4";
my $database="dbname";
my $user="user";
my $pw="pass";
my $table="table";    

I imagine I have to set up a tunnel through the gateway server to the database server. How do I go about doing that? If the MySQL database were on the gateway, I could open a tunnel like so:

$ ssh -f user@gateway -L 3307:127.0.0.1:3306 -N 

How can I modify this to tunnel through the open port 24222 on the gateway through to the MySQL server on 1.2.3.4?

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UPDATE:

Using @anttir's answer I got it to work as follows.

1. Set up the tunnel:

   $ ssh -fN -p 24222 [email protected] -L 3307:1.2.3.4:3306
   

2. Set up the script variables:

   my $host="127.0.0.1";
   my $port = 3307;
   

Answer 1

With the command:

$ ssh -f user@gateway -L 3307:1.2.3.4:3306 -N 

This states that all connections to client localhost 3307 will be forwarded via the SSH tunnel to gateway and then connected to host 1.2.3.4 to port 3306.

edit: If the SSH is on port 24222 then

$ ssh -f user@gateway -p 24222 -L 3307:1.2.3.4:3306 -N