Twelve balls are numbered by the numbers $1,2,3,\cdots,12$. Each ball is colored either red or green, so that the following two conditions are satisfied: (i) If two balls marked by different numbers $a$ and $b$ are colored red and $a+b<13$, then the ball marked by the number $a+b$ is colored red, too. (ii) If two balls marked by different numbers $a$ and $b$ are colored green and $a+b<13$, then the ball marked by the number $a+b$ is also colored green. How many ways are there of coloring the balls? Please remember to hide your solution. (by using the hide tags of course.. I don't literally mean that you should hide it )