<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 {
private:
    const int mod = 1e9 + 7;
    map<int, int> next, prev;
    vector<vector<long long>> dp;  // Use long long for larger values

    int solver(const string& str, int i, int j) {
        if (i > j) return 0;
        if (i == j) return 1;

        if (dp[i][j] != -1) return dp[i][j];

        long long count = 0;

        if (str[i] == str[j]) {
            int nextIdx = next[i];
            int prevIdx = prev[j];

            if (nextIdx < prevIdx) {
                count = (2 * solver(str, i + 1, j - 1) % mod - solver(str, nextIdx + 1, prevIdx - 1) % mod + mod) % mod;
            } else if (nextIdx == prevIdx) {
                count = (2 * solver(str, i + 1, j - 1) % mod + 1) % mod;
            } else {
                count = (2 * solver(str, i + 1, j - 1) % mod + 2) % mod;
            }
        } else {
            count = (solver(str, i + 1, j) % mod + solver(str, i, j - 1) % mod - (long long int)solver(str, i + 1, j - 1) % mod + mod) % mod;
        }

        return dp[i][j] = count;
    }

public:
    int countPalindromicSubsequences(const string& s) {
        int n = s.length();
        dp.resize(n, vector<long long>(n, -1));  // Use long long for dp array
        vector<int> arr(26, -1);  // Fixed size for 26 letters

        for (int i = 0; i < n; ++i) {
            char ch = s[i];
            if (arr[ch - 'a'] != -1) {
                next[arr[ch - 'a']] = i;
                prev[i] = arr[ch - 'a'];
            }
            arr[ch - 'a'] = i;
        }

        return solver(s, 0, n - 1);
    }
};

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