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.