<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>

from copy import deepcopy

mod = 1e9 + 7

class Solution:
    def countPalindromes(self, s: str) -> int:
        n = len(s)
        single_left = defaultdict(int)
        double_left = defaultdict(int)
        single_right = defaultdict(int)
        double_right = defaultdict(int)
        left_dp = []
        right_dp = []
        
        for char in s:
            for digit, count in single_left.items():
                double_left[digit+char] = int((double_left[digit+char] + count) % mod)

            single_left[char] += 1
            left_dp.append(deepcopy(double_left))
        
        
        for char in s[::-1]:
            for digit, count in single_right.items():
                double_right[digit+char] = int((double_right[digit+char] + count) % mod)

            single_right[char] += 1
            right_dp.append(deepcopy(double_right))
        right_dp = right_dp[::-1]

        ret = 0
        for i in range(1, n - 1):
            cur_left = left_dp[i - 1]
            cur_right = right_dp[i + 1]
            all_keys = set(list(cur_left.keys()) + list(cur_right.keys()))
            for key in all_keys:
                ret = int((ret + (cur_left[key] * cur_right[key]) % mod) % mod)
        
        return ret
88700