<p>You are given a string <code>word</code> and an array of strings <code>forbidden</code>.</p>

<p>A string is called <strong>valid</strong> if none of its substrings are present in <code>forbidden</code>.</p>

<p>Return <em>the length of the <strong>longest valid substring</strong> of the string </em><code>word</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters in a string, possibly empty.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> word = &quot;cbaaaabc&quot;, forbidden = [&quot;aaa&quot;,&quot;cb&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 11 valid substrings in word: &quot;c&quot;, &quot;b&quot;, &quot;a&quot;, &quot;ba&quot;, &quot;aa&quot;, &quot;bc&quot;, &quot;baa&quot;, &quot;aab&quot;, &quot;ab&quot;, &quot;abc&quot; and &quot;aabc&quot;. The length of the longest valid substring is 4. 
It can be shown that all other substrings contain either &quot;aaa&quot; or &quot;cb&quot; as a substring. </pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> word = &quot;leetcode&quot;, forbidden = [&quot;de&quot;,&quot;le&quot;,&quot;e&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 11 valid substrings in word: &quot;l&quot;, &quot;t&quot;, &quot;c&quot;, &quot;o&quot;, &quot;d&quot;, &quot;tc&quot;, &quot;co&quot;, &quot;od&quot;, &quot;tco&quot;, &quot;cod&quot;, and &quot;tcod&quot;. The length of the longest valid substring is 4.
It can be shown that all other substrings contain either &quot;de&quot;, &quot;le&quot;, or &quot;e&quot; as a substring. 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= word.length &lt;= 10<sup>5</sup></code></li>
	<li><code>word</code> consists only of lowercase English letters.</li>
	<li><code>1 &lt;= forbidden.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= forbidden[i].length &lt;= 10</code></li>
	<li><code>forbidden[i]</code> consists only of lowercase English letters.</li>
</ul>

class Trie:

    def __init__(self, *words):
        self.root = {}
        for word in words:
            self.insert(word)

    def insert(self, word: str) -> None:
        d = self.root
        for letter in word:
            d = d.setdefault(letter, {})
        d["_end_"] = True


    def search(self, word: str) -> bool:
        d = self.root
        for letter in word:
            if letter not in d:
                return False
            d = d[letter]
        return "_end_" in d

    def delitem(self, word: str) -> None:
        d = self.root
        nodes = [d]
        for letter in word:
            d = d[letter]
            nodes.append(d)
        del d["_end_"]

    
    def startsWith(self, prefix: str) -> bool:
        d = self.root
        for letter in prefix:
            if letter not in d:
                return False
            d = d[letter]


class Solution:
    def longestValidSubstring(self, word: str, forbidden: List[str]) -> int:
        N = len(word)
        T = Trie(*forbidden)
        ans = 0
        r = N

        for i in range(N-1, -1, -1):
            for k in range(1, 11):
                if i + k <= N:
                    if T.search(word[i: i+k]):
                        ans = max(ans, r-i-1)
                        r = min(r, i + k - 1)
                        break

            # print(f"i={i}, r={r}, ans={ans}")

        ans = max(ans, r)

        return ans


        
        
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