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Saiyans and halfbreeds possess the ability to transform into a form known
as that of a Super Saiyan. This form is actually divided into four stages,
known simply as SSJ, SSJ2, SSJ3, and SSJ4. Though all those with any saiyan
blood at all may attempt this transformation, only those that are truly
powerful will survive the process. When a saiyan or halfbreed turns into a 
Super Saiyan, they are surrounded by a glowing golden ki energy. In addition,
their hair often grows long and yellow. Rumors persist that there are ways
of identifying someone who has achieved a higher form of Super Saiyan,
but one would have to find out for oneself. And that might be dangerous.

There is a rumour that one can get Legendary Super Saiyan.

(SSJ1) Threshold: 150 Rage Modifier: 4
(SSJ2) Threshold: 350 Rage - PL 10,000,000 Modifier: 7
(SSJ3) Threshold: 550 Rage - PL 25,000,000 Modifier: 9
(SSJ4) Threshold: ??? Rage - PL 95,000,000 Modifier: 10

Stat Mods:
(SSJ1) - Str +2%, Int -1%
(SSJ2) - Str +4%, Int +2%, Dex +2%
(SSJ3) - Str +6%, Int -2%, Dex +2%
(SSJ4) - Str +6%, Int -3%, Dex +2%

Syntax: ssj # - transform into the form numbers you state, after training
        ssj - revert back to your normal state