<p>Given a string of digits <code>s</code>, return <em>the number of <strong>palindromic subsequences</strong> of</em> <code>s</code><em> having length </em><code>5</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p><strong>Note:</strong></p>

<ul>
	<li>A string is <strong>palindromic</strong> if it reads the same forward and backward.</li>
	<li>A <strong>subsequence</strong> is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.</li>
</ul>

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

<pre>
<strong>Input:</strong> s = &quot;103301&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
There are 6 possible subsequences of length 5: &quot;10330&quot;,&quot;10331&quot;,&quot;10301&quot;,&quot;10301&quot;,&quot;13301&quot;,&quot;03301&quot;. 
Two of them (both equal to &quot;10301&quot;) are palindromic.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;0000000&quot;
<strong>Output:</strong> 21
<strong>Explanation:</strong> All 21 subsequences are &quot;00000&quot;, which is palindromic.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;9999900000&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> The only two palindromic subsequences are &quot;99999&quot; and &quot;00000&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>4</sup></code></li>
	<li><code>s</code> consists of digits.</li>
</ul>

class Solution:
    def countPalindromes(self, s: str) -> int:
        n = len(s)
        mod = 10 ** 9 + 7
        s = [int(i) for i in s]

        memo = [[[[-1] * 5 for _ in range(10)] for _ in range(10)] for _ in range(n)]

        def rec(index, a1, a2, windex):
            if windex >= 5:
                return 1

            if index >= n:
                return 0

            if memo[index][a1][a2][windex] != -1:
                return memo[index][a1][a2][windex]

            ans = 0

            if windex <= 2:
                if windex == 0:
                    ans += rec(index + 1, s[index], a2, windex + 1)
                elif windex == 1:
                    ans += rec(index + 1, a1, s[index], windex + 1)
                else:
                    ans += rec(index + 1, a1, a2, windex + 1)
                
                ans += rec(index + 1, a1, a2, windex)
            else:
                comp = 5 - windex - 1
                compare = a1 if comp == 0 else a2

                if s[index] == compare:
                    ans += rec(index + 1, a1, a2, windex + 1)
                ans += rec(index + 1, a1, a2, windex)
            
            memo[index][a1][a2][windex] = ans % mod
            return memo[index][a1][a2][windex]

        return rec(0, 0, 0, 0) % mod
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