<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 evaluate(char opr,vector<bool> exp){

        if(opr == '!'){
            return !exp[0];
        }
        else if(opr == '&'){
            if(exp.size() == 1) return exp[0];
            for(int i=0 ; i<exp.size(); i++){
                if(exp[i] == false) return 0;
            }
            return 1;
        }
        else{
            if(exp.size() == 1) return exp[0];
            for(int i=0 ; i<exp.size(); i++){
                if(exp[i] == true) return 1;
            }
            return 0;
        }
    }
    bool parseBoolExpr(string s) {

        stack<char> opr;
        stack<char> val;

        s = '('+s+')';

        for(int i=0 ; i<s.size() ; i++)
        {
            if(s[i] == '|' || s[i] == '!' || s[i] == '&') opr.push(s[i]);
            else if(s[i] == '(' || s[i] == 'f' || s[i] == 't') val.push(s[i]);
            else if(s[i] == ')'){

                if(opr.empty()){ continue;}
                char operate = opr.top();
                opr.pop();

                vector<bool> exp; 
                
                while(val.top() != '(') {
                    
                    if(val.top() == 'f') exp.push_back(false);
                    else if(val.top() == 't') exp.push_back(true);
                    val.pop();
                    }
                val.pop();
                if(evaluate(operate,exp))
                val.push('t');
                else val.push('f');

            }
        }

        // char operate = opr.top();
        // opr.pop();

        // vector<bool> exp; 
        
        // while(!val.empty()) {
            
        //     if(val.top() == 'f') exp.push_back(false);
        //     else if(val.top() == 't') exp.push_back(true);
        //     val.pop();
        //     }
        
        // return e

        return val.top() == 't' ? true : false;
           
    }
};
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