Given a boolean expression consisting of the symbols 0 (false), 1 (true), & (AND), | (OR), and ^ (XOR), and a desired boolean result value result, implement a function to count the number of ways of parenthesizing the expression such that it evaluates to result.
Example 1:
Input: s = "1^0|0|1", result = 0 Output: 2 Explanation: Two possible parenthesizing ways are: 1^(0|(0|1)) 1^((0|0)|1)
Example 2:
Input: s = "0&0&0&1^1|0", result = 1 Output: 10
Note:
- There are no more than 19 operators in
s.