<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>

class Solution {
public:
    int countPalindromicSubsequences(string s) {
        int n = s.length();
        vector<vector<vector<long long>>> memo(4, vector<vector<long long>>(n, vector<long long>(n, -1)));
        return countPalindromicSubsequencesHelper(s, 0, n - 1, memo);
    }
    
private:
    const int MOD = 1e9 + 7;
    
    long long countPalindromicSubsequencesHelper(const string& s, int start, int end, vector<vector<vector<long long>>>& memo) {
        if (start > end) return 0;
        if (start == end) return 1;
        
        long long result = 0;
        for (int i = 0; i < 4; i++) {
            char c = 'a' + i;
            if (memo[i][start][end] != -1) {
                result = (result + memo[i][start][end]) % MOD;
            } else {
                int left = start;
                int right = end;
                
                while (left <= end && s[left] != c) left++;
                while (right >= start && s[right] != c) right--;
                
                if (left > right) {
                    memo[i][start][end] = 0;
                } else if (left == right) {
                    memo[i][start][end] = 1;
                } else {
                    memo[i][start][end] = (2 + countPalindromicSubsequencesHelper(s, left + 1, right - 1, memo)) % MOD;
                }
                
                result = (result + memo[i][start][end]) % MOD;
            }
        }
        
        return result;
    }
};
80710