<p>A <strong>valid encoding</strong> of an array of <code>words</code> is any reference string <code>s</code> and array of indices <code>indices</code> such that:</p>

<ul>
	<li><code>words.length == indices.length</code></li>
	<li>The reference string <code>s</code> ends with the <code>&#39;#&#39;</code> character.</li>
	<li>For each index <code>indices[i]</code>, the <strong>substring</strong> of <code>s</code> starting from <code>indices[i]</code> and up to (but not including) the next <code>&#39;#&#39;</code> character is equal to <code>words[i]</code>.</li>
</ul>

<p>Given an array of <code>words</code>, return <em>the <strong>length of the shortest reference string</strong> </em><code>s</code><em> possible of any <strong>valid encoding</strong> of </em><code>words</code><em>.</em></p>

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

<pre>
<strong>Input:</strong> words = [&quot;time&quot;, &quot;me&quot;, &quot;bell&quot;]
<strong>Output:</strong> 10
<strong>Explanation:</strong> A valid encoding would be s = <code>&quot;time#bell#&quot; and indices = [0, 2, 5</code>].
words[0] = &quot;time&quot;, the substring of s starting from indices[0] = 0 to the next &#39;#&#39; is underlined in &quot;<u>time</u>#bell#&quot;
words[1] = &quot;me&quot;, the substring of s starting from indices[1] = 2 to the next &#39;#&#39; is underlined in &quot;ti<u>me</u>#bell#&quot;
words[2] = &quot;bell&quot;, the substring of s starting from indices[2] = 5 to the next &#39;#&#39; is underlined in &quot;time#<u>bell</u>#&quot;
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;t&quot;]
<strong>Output:</strong> 2
<strong>Explanation:</strong> A valid encoding would be s = &quot;t#&quot; and indices = [0].
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 2000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 7</code></li>
	<li><code>words[i]</code> consists of only lowercase letters.</li>
</ul>

class Tries:
    def __init__(self):
        self.data = dict()
        self.is_end=False
        self.idx = -1
    def add(self,word:str, idx:int, parent: List[int]) ->None:
        """
        Add word
        """
        cur = self
        for ch in word:
            if ch in cur.data:
                cur = cur.data[ch]
                if cur.is_end:
                    parent[cur.idx] = idx
            else:
                cur.data[ch] = Tries()
                cur = cur.data[ch]
        cur.is_end=True
        cur.idx = idx

class Solution:
    def minimumLengthEncoding(self, words: List[str]) -> int:
        n = len(words)
        root = Tries()
        parent = [i for i in range(n)]
        for word, idx in sorted(zip(words, range(n)), key = lambda x:( len(x[0]), x[1]) ):
            root.add(word[::-1], idx, parent)
        
        def find(idx:int)-> int:
            if parent[idx] != idx:
                parent[idx] = find(parent[idx])
            return parent[idx]
        unique_idx = [find(i) for i in range(n)]
        return sum(len(words[i])+1 for i in set(unique_idx))
19800