Nestings

Many different technical languages use nestings to convey some sort of meaning. Mathematics uses parentheses and brackets very often in expressions to group values. Your method will test whether a given nesting is valid, and if it is, how deep it goes.
To be valid, a nesting must obey the following criteria (quotes for clarity):
1) Every left marker has a CORRECTLY matching right marker (i.e. every '[' has a ']'; described in table below)
2) Nestings cannot be interwoven. (e.g. "{[}]" is not a valid nesting since {} and [] are interwoven) In other words, a right marker must be CORRECTLY matched by the left marker immediately preceding it, which has not already been matched.
3) Every nesting marker in the string must delimit a nesting. All other characters must be letters. For example, "{[}" isn't valid since '[' is a marker that does not delimit a nesting. "asdJLBasdf" is valid since letters can exist anywhere in the string.
The CORRECTLY matched nesting markers are:

Left         Right
<             >
(             )
[             ]
{             }
/*            */

If there is an invalid nesting your method will return -1. Otherwise you will return the deepest nesting level in the input. For example:
Nesting-wise explanations will use numbers to depict nesting depths throughout the given strings.
nested = "" no nestings so deepest nesting level is 0
nested = "<(A)(b)>" nesting-wise this looks like <1(2)1(2)1> so the deepest level would be 2
nested = "<()()>" nesting-wise this looks like <1(2)1(2)1> so the deepest level would be 2
nested = "(/*/)" is invalid(-1) since /* is a valid left marker but the / left over is not a valid marker
nested = "(*)" is invalid(-1) since * is not a letter and it isn't used as part of a nesting marker
As seen in examples above, the nesting depth at any point in a string measures how many sets of markers you are between. If the nesting is valid, your method returns the highest nesting depth occuring in the input string.

Create a class Nestings that contains the method howDeep, which takes a String nested, and returns an int describing the deepest nesting level or -1 if it is invalid.