Zhang3 has made a fake photo by Photoshop, and published it on the Internet.
However, there are $n$ watches in the photo, showing different times. We assume that every watch has two hands: the hour hand and the minute hand, both moves at a uniform speed.
Someone pointed out the problem of the watches. Then everyone began to doubt that it's a fake photo. To respond, Zhang3 will announce that the photo is taken at time $x$, which is a time in a day. By choosing $x$ perfectly, she can make all of the watches look like showing time $x$, with a small error. For example, if there are two watches showing $\text{12:30:00}$ and $\text{02:40:00}$ respectively, she can choose $x = \text{01:35:00}$ as if both watches are showing time $x$.
Specifically, we define the error of a hand of a watch as the angle between its actual location and its ideal location, where the ideal location is the correct location to show time $x$. In the example above, the first watch shows $\text{12:30:00}$ and $x = \text{01:35:00}$, so the minute hand has an error of $30^\circ$ while the error of the hour hand is a little bit larger.
Please help Zhang3 choose such $x$ that the maximum error among all of the $2n$ hands is minimized. $x$ doesn't need to be an integer in seconds. Print the optimal error in degrees.