<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:
    static const constexpr int64_t kMod = 1e9 + 7;
    inline int64_t module(int x) {
        return x > kMod ? x - kMod : (x < 0 ? x + kMod : x);
    }

public:
    Solution() {
        ios_base::sync_with_stdio(false);
        cin.tie(0);
        cout.tie(0);
        cout.setf(ios::fixed);
        cout.setf(ios::showpoint);
        cout.precision(20); 
    }


    int countPalindromicSubsequences(const string& s) {
        const size_t sz = s.size();
        int64_t dp[sz][2];
        for_each(dp, dp + sz, [](auto& v) { fill(v, v + 2, 0); });
        int64_t res = 0;
        for (int i = 0; i < sz; ++i) {
            int64_t pre = 1;
            for (int j = i - 1; j >= 0; --j) {
                if (s[j] == s[i]) {
                    int64_t x = dp[j][0] + 1;
                    dp[j][0] = module(dp[j][0] + pre);
                    pre = module(x - dp[j][1]);
                    dp[j][1] = x;
                } else {
                    dp[j][0] = module(dp[j][0] + pre);
                }
            }
            res = module(res + pre);
        }
        return res;
    }
};

9864