How to Jailbreak my old iPod Touch 1G?

1. I forgot that it has been a long time since I updated by Jailbroken iPod Touch 1G which is on Firmware 2.1.1
2. Cydia no longer is able to update all the latest patches. It seems that I have 34 files/apps need to upgraded.
3. Since, Cydia failed to update, I have decided to Restore to 2.2.1 and Jailbreak it.
4. Then, I realized Blackra1n did not support 2.2.1.
5. Thus, I downloaded 3.1.3 and Jailbreak it using Jailbreakme.com.