<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 orOp(bool eval, stack<bool> &temp)
    {
        while(!temp.empty())
        {
            eval = eval || temp.top();
            temp.pop();
        }

        return eval;
    }

    bool andOp(bool eval, stack<bool> &temp)
    {
        while(!temp.empty())
        {
            eval = eval && temp.top();
            temp.pop();
        }

        return eval;
    }

    bool parseBoolExpr(string s) 
    {
        int n = s.length();
        stack<char> st;
        bool res = false;

        int i = 0;
        while(i != n)
        {
            if(s[i] == '&' || s[i] == '!' || s[i] == '|' || s[i] == 't' || s[i] == 'f')
            {
                st.push(s[i]);
                ++i;
            }

            else if(s[i] == '(' || s[i] == ',')
            ++i;

            else if(s[i] == ')')
            {
                stack<bool> temp;
                while(st.top() != '|' && st.top() != '&' && st.top() != '!')
                {
                    char ch = st.top();
                    st.pop();

                    if(ch == 'f')
                    temp.push(false);

                    else if(ch == 't')
                    temp.push(true);
                }

                char op = st.top();
                st.pop();

                bool eval = temp.top();
                temp.pop();

                if(op == '!')
                eval = !eval;

                // if only one character was present
                if(temp.empty())
                {
                    res = eval;
                    st.push((eval) ? 't' : 'f');
                    ++i;
                    continue;
                }

                if(op == '&')
                eval = andOp(eval, temp);

                if(op == '|')
                eval = orOp(eval, temp);

                res = eval;
                st.push((eval) ? 't' : 'f');
                ++i;
            }
        }

        return res;      
    }
};
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