<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 doOperation(bool val1, bool val2, char currOp) {
        if (currOp == '!') {
            return !val1;
        }

        if (currOp == '&') {
            return val1 & val2;
        }

        return val1 | val2;
    }

    bool solveExpression(int &currIdx, int n, string& s) {
        // cout<<currIdx<<" "<<n<<endl;
        char currOperation = s[currIdx];
        currIdx += 2;
        stack<bool> store;

        while (s[currIdx] != ')' and currIdx < n) {
            if (s[currIdx] == 't' or s[currIdx] == 'f') { //  if true or false
                bool val = (s[currIdx] == 't' ? true : false);
                store.push(val);
            } else if (s[currIdx] == '!' or s[currIdx] == '|' or
                       s[currIdx] == '&') { //  operator
                bool val =
                    solveExpression(currIdx , n , s);
                    store.push(val);
            }
           currIdx++; 
        }

        // currIdx -= 2;    
        bool curr = false, prev = false;
        bool firstTime = true;
        while (!store.empty()) {
            curr = store.top();
            store.pop();
            if (firstTime) {
                prev = curr;
                firstTime = false;
            }
            prev = doOperation(curr, prev, currOperation);
        }

      
        return prev;
    }

    bool parseBoolExpr(string expression) {
        if (expression == "t") {
            return true;
        }

        if (expression == "f") {
            return false;
        }
        int n = expression.size();
        int currIdx = 0; 
        return solveExpression(currIdx, n, expression);
    }
};
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