<p>A <strong>boolean expression</strong> is an expression that evaluates to either <code>true</code> or <code>false</code>. It can be in one of the following shapes:</p>

<ul>
	<li><code>&#39;t&#39;</code> that evaluates to <code>true</code>.</li>
	<li><code>&#39;f&#39;</code> that evaluates to <code>false</code>.</li>
	<li><code>&#39;!(subExpr)&#39;</code> that evaluates to <strong>the logical NOT</strong> of the inner expression <code>subExpr</code>.</li>
	<li><code>&#39;&amp;(subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub>)&#39;</code> that evaluates to <strong>the logical AND</strong> of the inner expressions <code>subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub></code> where <code>n &gt;= 1</code>.</li>
	<li><code>&#39;|(subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub>)&#39;</code> that evaluates to <strong>the logical OR</strong> of the inner expressions <code>subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub></code> where <code>n &gt;= 1</code>.</li>
</ul>

<p>Given a string <code>expression</code> that represents a <strong>boolean expression</strong>, return <em>the evaluation of that expression</em>.</p>

<p>It is <strong>guaranteed</strong> that the given expression is valid and follows the given rules.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;&amp;(|(f))&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> 
First, evaluate |(f) --&gt; f. The expression is now &quot;&amp;(f)&quot;.
Then, evaluate &amp;(f) --&gt; f. The expression is now &quot;f&quot;.
Finally, return false.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;|(f,f,f,t)&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> The evaluation of (false OR false OR false OR true) is true.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;!(&amp;(f,t))&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> 
First, evaluate &amp;(f,t) --&gt; (false AND true) --&gt; false --&gt; f. The expression is now &quot;!(f)&quot;.
Then, evaluate !(f) --&gt; NOT false --&gt; true. We return true.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= expression.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li>expression[i] is one following characters: <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code>, <code>&#39;&amp;&#39;</code>, <code>&#39;|&#39;</code>, <code>&#39;!&#39;</code>, <code>&#39;t&#39;</code>, <code>&#39;f&#39;</code>, and <code>&#39;,&#39;</code>.</li>
</ul>

class Solution {
public:

    bool parse_or(string ops) {
        int n = ops.size();
        bool ans = false;  // Initialize for OR
        for (int i = 0; i < n; i++) {
            ans |= (ops[i] == 't');
        }
        return ans;
    }

    bool parse_and(string ops) {
        int n = ops.size();
        bool ans = true;  // Initialize for AND
        for (int i = 0; i < n; i++) {
            ans &= (ops[i] == 't');
        }
        return ans;
    }

    bool parse_not(string ops) {
        return !(ops[0] == 't');  // Return negation
    }

    bool parseBoolExpr(string exp) {
        stack<char> st;

        for (auto el : exp) {
            if (el == 'f' || el == 't' || el == '!' || el == '|' || el == '&') {
                st.push(el);
            }
            if (el == ')') {
                string ops = "";
                while (!st.empty() && st.top() != '!' && st.top() != '|' && st.top() != '&' && st.top() != '(') {
                    ops += st.top();
                    st.pop();
                }
                char oper = st.top();
                st.pop();  // Pop the operator or '('
                bool res;
                if (oper == '|') res = parse_or(ops);
                else if (oper == '&') res = parse_and(ops);
                else if (oper == '!') res = parse_not(ops);
                // After parsing, push the result as 't' or 'f'
                st.push(res ? 't' : 'f');
            }
        }

        // The final result will be 't' or 'f' at the top of the stack
        return st.top() == 't';
    }
};

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