You need to ssh through jumphosts host02 and host03 to get to host04 .

Edit your OpenSSH configuration file
[host01]# vim $HOME/.ssh/config
…with the following
host host03
proxycommand ssh -q -AW %h:%p host02
host host04
proxycommand ssh -q -AW %h:%p host03
Setup ssh keys
[host01]# ls $HOME/.ssh/id_rsa 2> /dev/null || ssh-keygen -t rsa
Copy the public key to the servers for automatic login
[host01]# ssh-copy-id $USER@host02
[host01]# ssh-copy-id $USER@host03
[host01]# ssh-copy-id $USER@host04
Test
[host01]# ssh host04
[host04]#
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