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

        if (expression == "f") {
            return false;
        }

        if (expression[0] == '!') {
            return !parseBoolExpr(expression.substr(2, expression.size() - 3));
        }

        char logicalOp = expression[0];
        if (logicalOp == '!') {
            return !parseBoolExpr(expression.substr(2, expression.size() - 3));
        }

        vector<string> subExprs;
        // &(subExpr1, subExpr2) => subExpr1, subExpr2
        expression = expression.substr(2, expression.size() - 3);
        pair<string, string> currExprWithRestExprs = {"", expression};
        while (!currExprWithRestExprs.second.empty()) {
            currExprWithRestExprs = eatExpr(currExprWithRestExprs.second);
            subExprs.push_back(currExprWithRestExprs.first);

            while (!currExprWithRestExprs.second.empty() && currExprWithRestExprs.second[0] == ',') {
                currExprWithRestExprs.second = currExprWithRestExprs.second.substr(1);
            }
        }

        if (logicalOp == '&') {
            for (auto subExpr : subExprs) {
                // cout << subExpr << endl;
                if (!parseBoolExpr(subExpr)) 
                    return false;
            }
            return true;
        }

        // logicalOp == '|'
        for (auto subExpr : subExprs) {
            // cout << subExpr << endl;
            if (parseBoolExpr(subExpr)) 
                return true;
        }
        return false;
    }

    pair<string, string> eatExpr(const string& exprArr) {
        if (exprArr[0] == 't' || exprArr[0] == 'f') {
            string res = exprArr[0] == 't' ? "t" : "f";
            return {res, exprArr.substr(1)};
        }

        int bracketPairCounter = 1;
        for (int i = 2; i < exprArr.size(); i++) {
            if (exprArr[i] == '(')
                bracketPairCounter++;
            else if (exprArr[i] == ')')
                bracketPairCounter--;

            if (bracketPairCounter == 0)
                return {exprArr.substr(0, i + 1), exprArr.substr(i + 1)};
        }
        return {};
    }
};
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