<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 {
    pair<bool, int> parseExpression(string& s, int ind, int n, char oper) {
        if (s[ind] == 't') return {true, ind+1};
        if (s[ind] == 'f') return {false, ind+1};

        stack<char> st;
        st.push('(');
        vector<bool> result;
        int i = ind+1;
        while(!st.empty() && i < n) {
            if (s[i] == '&' || s[i] == '|' || s[i] == '!') {
                pair<bool, int> ans = parseExpression(s, i+1, n, s[i]);
                i = ans.second;
                result.push_back(ans.first);
            } else if (s[i] == 't') {
                result.push_back(true);
            } else if (s[i] == 'f') {
                result.push_back(false);
            } else if (s[i] == ')') {
                st.pop();
                continue;
            }
            i++;
        }

        bool ans;
        if (oper == '&') {
            ans = true;
            for (bool el : result) {
                ans = ans & el;
            }
        } else if (oper == '|') {
            ans = false;
            for (bool el : result) {
                ans = ans | el;
            }
        } else {
            ans = !(result[0]);
        }

        return {ans, i};
    }
public:
    bool parseBoolExpr(string s) {
        int n = s.length();
        if (s[0] == 't') return true;
        if (s[0] == 'f') return false;
        return parseExpression(s, 1, n, s[0]).first;
    }
};
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