<p>Given a string <code>s</code> containing only three types of characters: <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code> and <code>&#39;*&#39;</code>, return <code>true</code> <em>if</em> <code>s</code> <em>is <strong>valid</strong></em>.</p>

<p>The following rules define a <strong>valid</strong> string:</p>

<ul>
	<li>Any left parenthesis <code>&#39;(&#39;</code> must have a corresponding right parenthesis <code>&#39;)&#39;</code>.</li>
	<li>Any right parenthesis <code>&#39;)&#39;</code> must have a corresponding left parenthesis <code>&#39;(&#39;</code>.</li>
	<li>Left parenthesis <code>&#39;(&#39;</code> must go before the corresponding right parenthesis <code>&#39;)&#39;</code>.</li>
	<li><code>&#39;*&#39;</code> could be treated as a single right parenthesis <code>&#39;)&#39;</code> or a single left parenthesis <code>&#39;(&#39;</code> or an empty string <code>&quot;&quot;</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "()"
<strong>Output:</strong> true
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "(*)"
<strong>Output:</strong> true
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> s = "(*))"
<strong>Output:</strong> true
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 100</code></li>
	<li><code>s[i]</code> is <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code> or <code>&#39;*&#39;</code>.</li>
</ul>

class Solution:
    def checkValidString(self, s: str) -> bool:
        numberSet = set()
        numberSet.add((0,0))
        for character in s:
            newNumberSet = set()
            if character == "(":
                for (l, r) in numberSet:
                    newNumbers = (l+1, r)
                    newNumberSet.add(newNumbers)
            if character == ")":
                for (l, r) in numberSet: 
                    if r + 1 <= l:
                        newNumbers = (l, r+1)
                        newNumberSet.add(newNumbers)
            if character == "*":
                for (l, r) in numberSet: 
                    newNumberSet.add((l, r))
                    newNumberSet.add((l +1, r))
                    if r + 1 <= l:
                        newNumberSet.add((l, r+1))
            if (len(newNumberSet)) == 0:
                return False
            numberSet = newNumberSet
        
        for (l, r) in newNumberSet:
            if l == r:
                return True
        
        return False
                     

        
                        
        
17000