<p>You are given a <strong>0-indexed</strong> string array <code>words</code>.</p>

<p>Let&#39;s define a <strong>boolean</strong> function <code>isPrefixAndSuffix</code> that takes two strings, <code>str1</code> and <code>str2</code>:</p>

<ul>
	<li><code>isPrefixAndSuffix(str1, str2)</code> returns <code>true</code> if <code>str1</code> is <strong>both</strong> a <span data-keyword="string-prefix">prefix</span> and a <span data-keyword="string-suffix">suffix</span> of <code>str2</code>, and <code>false</code> otherwise.</li>
</ul>

<p>For example, <code>isPrefixAndSuffix(&quot;aba&quot;, &quot;ababa&quot;)</code> is <code>true</code> because <code>&quot;aba&quot;</code> is a prefix of <code>&quot;ababa&quot;</code> and also a suffix, but <code>isPrefixAndSuffix(&quot;abc&quot;, &quot;abcd&quot;)</code> is <code>false</code>.</p>

<p>Return <em>an integer denoting the <strong>number</strong> of index pairs </em><code>(i<em>, </em>j)</code><em> such that </em><code>i &lt; j</code><em>, and </em><code>isPrefixAndSuffix(words[i], words[j])</code><em> is </em><code>true</code><em>.</em></p>

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

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;aba&quot;,&quot;ababa&quot;,&quot;aa&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> In this example, the counted index pairs are:
i = 0 and j = 1 because isPrefixAndSuffix(&quot;a&quot;, &quot;aba&quot;) is true.
i = 0 and j = 2 because isPrefixAndSuffix(&quot;a&quot;, &quot;ababa&quot;) is true.
i = 0 and j = 3 because isPrefixAndSuffix(&quot;a&quot;, &quot;aa&quot;) is true.
i = 1 and j = 2 because isPrefixAndSuffix(&quot;aba&quot;, &quot;ababa&quot;) is true.
Therefore, the answer is 4.</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;pa&quot;,&quot;papa&quot;,&quot;ma&quot;,&quot;mama&quot;]
<strong>Output:</strong> 2
<strong>Explanation:</strong> In this example, the counted index pairs are:
i = 0 and j = 1 because isPrefixAndSuffix(&quot;pa&quot;, &quot;papa&quot;) is true.
i = 2 and j = 3 because isPrefixAndSuffix(&quot;ma&quot;, &quot;mama&quot;) is true.
Therefore, the answer is 2.  </pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;abab&quot;,&quot;ab&quot;]
<strong>Output:</strong> 0
<strong>Explanation: </strong>In this example, the only valid index pair is i = 0 and j = 1, and isPrefixAndSuffix(&quot;abab&quot;, &quot;ab&quot;) is false.
Therefore, the answer is 0.</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= words[i].length &lt;= 10<sup>5</sup></code></li>
	<li><code>words[i]</code> consists only of lowercase English letters.</li>
	<li>The sum of the lengths of all <code>words[i]</code> does not exceed <code>5 * 10<sup>5</sup></code>.</li>
</ul>


import random

DEFAULT_PRIME = 2**61 - 1
DEFAULT_ELEMENT = random.randint(2, DEFAULT_PRIME - 1)

class ProgressiveHash:
  def __init__(self, modulus = DEFAULT_PRIME, element = DEFAULT_ELEMENT):
      self.modulus = modulus
      self.element = element % modulus

      self.Reset()

  def Append(self, incoming):
      self.hash = (incoming + self.hash * self.element) % self.modulus
      self.shift_factor = (self.shift_factor * self.element) % self.modulus

      return self.hash
  
  def Prepend(self, incoming):
      self.hash = (self.hash + incoming * self.shift_factor) % self.modulus
      self.shift_factor = (self.shift_factor * self.element) % self.modulus

      return self.hash

  def GetHash(self):
      return self.hash        

  def Reset(self):
      self.hash = 0
      self.shift_factor = 1


class ForwardHash:
  def __init__(self, modulus = DEFAULT_PRIME, element = DEFAULT_ELEMENT):
      self.modulus = modulus
      self.element = element % modulus
      self.Reset()

  def Append(self, incoming):
      self.hash = (incoming + self.hash * self.element) % self.modulus
      return self.hash

  def GetHash(self):
      return self.hash        

  def Reset(self):
      self.hash = 0


def CheckAgainstHistory(word, history):
    prefix = ForwardHash()
    suffix = ProgressiveHash()

    count = 0

    W = [ ord(ch) for ch in word ]

    N = len(word)
    for i in range(N):
        ph = prefix.Append(W[i])
        sh = suffix.Prepend(W[-(i+1)])

        if ph == sh and ph in history:
            count += history[ph]

    history[ph] = history.get(ph, 0) + 1

    return count

def PrefixAndSuffix(words):
    history = {}

    total = 0
    for text in words:
        total += CheckAgainstHistory(text, history)

    return total

class Solution:
    def countPrefixSuffixPairs(self, words: List[str]) -> int:
        print([ len(W) for W in words ])
        return PrefixAndSuffix(words)

1633