A string is a valid parentheses string (denoted VPS) if it meets one of the following:
 It is an empty string
""
, or a single character not equal to"("
or")"
,  It can be written as
AB
(A
concatenated withB
), whereA
andB
are VPS's, or  It can be written as
(A)
, whereA
is a VPS.
We can similarly define the nesting depth depth(S)
of any VPS S
as follows:
depth("") = 0
depth(C) = 0
, whereC
is a string with a single character not equal to"("
or")"
.depth(A + B) = max(depth(A)
,depth(B))
, whereA
andB
are VPS's.depth("(" + A + ")") = 1 + depth(A)
, whereA
is a VPS.
For example, ""
, "()()"
, and "()(()())"
are VPS's (with nesting depths 0, 1, and 2), and ")("
and "(()"
are not VPS's.
Given a VPS represented as string s
, return the nesting depth of s
.
Example 1:
Input: s = "(1+(2*3)+((8)/4))+1"
Output: 3
Explanation: Digit 8 is inside of 3 nested parentheses in the string.
Example 2:
Input: s = "(1)+((2))+(((3)))"
Output: 3
Constraints:
1 <= s.length <= 100
s
consists of digits09
and characters'+'
,''
,'*'
,'/'
,'('
, and')'
. It is guaranteed that parentheses expression
s
is a VPS.

