A large stream blocks your path. According to the locals, it's not safe to cross the stream at the moment because it's full of garbage. You look down at the stream; rather than water, you discover that it's a stream of characters.
You sit for a while and record part of the stream (your puzzle input). The characters represent groups - sequences that begin with { and end with }. Within a group, there are zero or more other things, separated by commas: either another group or garbage. Since groups can contain other groups, a } only closes the most-recently-opened unclosed group - that is, they are nestable. Your puzzle input represents a single, large group which itself contains many smaller ones.
Sometimes, instead of a group, you will find garbage. Garbage begins with < and ends with >. Between those angle brackets, almost any character can appear, including { and }. Within garbage, < has no special meaning.
In a futile attempt to clean up the garbage, some program has canceled some of the characters within it using !: inside garbage, any character that comes after ! should be ignored, including <, >, and even another !.
You don't see any characters that deviate from these rules. Outside garbage, you only find well-formed groups, and garbage always terminates according to the rules above.
Here are some self-contained pieces of garbage:
<>, empty garbage.
<random characters>, garbage containing random characters.
<<<<>, because the extra < are ignored.
<{!>}>, because the first > is canceled.
<!!>, because the second ! is canceled, allowing the > to terminate the garbage.
<!!!>>, because the second ! and the first > are canceled.
<{o"i!a,<{i<a>, which ends at the first >.
Here are some examples of whole streams and the number of groups they contain:
{}, 1 group.
{{{}}}, 3 groups.
{{},{}}, also 3 groups.
{{{},{},{{}}}}, 6 groups.
{<{},{},{{}}>}, 1 group (which itself contains garbage).
{<a>,<a>,<a>,<a>}, 1 group.
{{<a>},{<a>},{<a>},{<a>}}, 5 groups.
{{<!>},{<!>},{<!>},{<a>}}, 2 groups (since all but the last > are canceled).
Your goal is to find the total score for all groups in your input. Each group is assigned a score which is one more than the score of the group that immediately contains it. (The outermost group gets a score of 1.)
To prove you've removed it, you need to count all of the characters within the garbage. The leading and trailing < and > don't count, nor do any canceled characters or the ! doing the canceling.
<>, 0 characters.
<random characters>, 17 characters.
<<<<>, 3 characters.
<{!>}>, 2 characters.
<!!>, 0 characters.
<!!!>>, 0 characters.
<{o"i!a,<{i<a>, 10 characters.
How many non-canceled characters are within the garbage in your puzzle input?
