<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 solve(string& expression, int index){

        if(index > expression.size())   return false;
        
        if(expression[index] == '&')    return AND(expression, ++index);
        if(expression[index] == '|')    return OR(expression, ++index);
        if(expression[index] == '!')    return NOT(expression, ++index);

        return expression[index]=='t'?true:false;

    }
    bool AND(string& expression, int& index){
        bool ans = true;
        while(expression[index] != ')'){
            // if(expression[index] == 't' || expression[index] == ',' || expression[index] == '(')    continue;
            if(expression[index] == 'f')    ans = false & ans;
            else if(expression[index] == '&')    ans = ans & AND(expression, ++index);
            else if(expression[index] == '|')    ans = ans & OR(expression, ++index);
            else if(expression[index] == '!')    ans = ans & NOT(expression, ++index);
            index++; 
        }
        return ans; 
    }
    bool OR(string& expression, int& index){
        bool ans = false;
        while(expression[index] != ')'){
            // if(expression[index] == 't' || expression[index] == ',' || expression[index] == '(')    continue;
            if(expression[index] == 't')    ans = true | ans;
            else if(expression[index] == '&')    ans = ans | AND(expression, ++index);
            else if(expression[index] == '|')    ans = ans | OR(expression, ++index);
            else if(expression[index] == '!')    ans = ans | NOT(expression, ++index);
            index++; 
        }
        return ans;
    }
    bool NOT(string& expression, int& index){
        index++;
        bool ans;
        if(expression[index] == 'f')        ans = !false;
        else if(expression[index] == 't')   ans = !true;
        else if(expression[index] == '&')    ans = !AND(expression, ++index);
        else if(expression[index] == '|')    ans = !OR(expression, ++index);
        else if(expression[index] == '!')    ans = !NOT(expression, ++index);
        index++;
        return ans;
    }

    bool parseBoolExpr(string expression) {
        
        if(expression[0] == 'f')    return false;
        else if(expression[0] == 't')   return true;

        return solve(expression,0);

    }
};
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