<p>Given a string s, return <em>the number of different non-empty palindromic subsequences in</em> <code>s</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>A subsequence of a string is obtained by deleting zero or more characters from the string.</p>

<p>A sequence is palindromic if it is equal to the sequence reversed.</p>

<p>Two sequences <code>a<sub>1</sub>, a<sub>2</sub>, ...</code> and <code>b<sub>1</sub>, b<sub>2</sub>, ...</code> are different if there is some <code>i</code> for which <code>a<sub>i</sub> != b<sub>i</sub></code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;bccb&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> The 6 different non-empty palindromic subsequences are &#39;b&#39;, &#39;c&#39;, &#39;bb&#39;, &#39;cc&#39;, &#39;bcb&#39;, &#39;bccb&#39;.
Note that &#39;bcb&#39; is counted only once, even though it occurs twice.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;abcdabcdabcdabcdabcdabcdabcdabcddcbadcbadcbadcbadcbadcbadcbadcba&quot;
<strong>Output:</strong> 104860361
<strong>Explanation:</strong> There are 3104860382 different non-empty palindromic subsequences, which is 104860361 modulo 10<sup>9</sup> + 7.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s[i]</code> is either <code>&#39;a&#39;</code>, <code>&#39;b&#39;</code>, <code>&#39;c&#39;</code>, or <code>&#39;d&#39;</code>.</li>
</ul>

import bisect


class Solution:
    def helper(self, stt, end, first):
        key = stt, end, first
        if key in self.mem:
            return self.mem[key]
        
        if stt == end:
            self.mem[key] = 1 if self.s[stt] == first else 0
            return self.mem[key]
        
        if first != self.s[stt]:
            self.mem[key] = self.helper(stt+1, end, first)
            return self.mem[key]
        
        r = 1
        l = self.c_to_i[self.s[stt]]
        mid = l[bisect.bisect_right(l, end)-1]
        assert mid >= stt
        if mid == stt:
            self.mem[key] = r
            return self.mem[key]
        
        r += 1
        if mid == stt+1:
            self.mem[key] = r
            return self.mem[key]
        
        for c in self.c_to_i:
            r += self.helper(stt+1, mid-1, c)
            r %= self.deno
        self.mem[key] = r
        return self.mem[key]

    def countPalindromicSubsequences(self, s: str) -> int:
        self.deno = 10 ** 9 + 7
        self.s = s
        self.c_to_i = {}
        for i, c in enumerate(s):
            self.c_to_i.setdefault(c, [])
            self.c_to_i[c].append(i)
        self.mem = {}
        rst = 0
        for c in self.c_to_i:
            rst += self.helper(0, len(s)-1, c)
            rst %= self.deno
        return rst
        
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