<p>Given a boolean expression consisting of the symbols <code>0</code> (false), <code>1</code> (true), <code>&</code> (AND), <code>|</code> (OR), and <code>^</code> (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.</p> <p><strong>Example 1:</strong></p> <pre> <strong>Input: </strong>s = "1^0|0|1", result = 0 <strong>Output: </strong>2 <strong>Explanation:</strong> Two possible parenthesizing ways are: 1^(0|(0|1)) 1^((0|0)|1) </pre> <p><strong>Example 2:</strong></p> <pre> <strong>Input: </strong>s = "0&0&0&1^1|0", result = 1 <strong>Output: </strong>10</pre> <p><strong>Note: </strong></p> <ul> <li>There are no more than 19 operators in <code>s</code>.</li> </ul>