<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>

int dp[1001][1001];
class Solution {
public:
    long long N=1e9+7;
    long long solve(int i, int j, string&s, map<char,set<int>> &mp)
    {
        int n=s.size();
        if(i==j) return 1;
        if(i>j) return 0;
        if(dp[i][j]!=-1) return dp[i][j];
        long long ans=0;
        if(s[i]!=s[j]) ans+=solve(i,j-1,s,mp)+solve(i+1,j,s,mp)-solve(i+1,j-1,s,mp),ans%=N;
        else
        {
           int nxt=n; int prev=-1;
           auto it=mp[s[i]].find(i); it++;
           if(it!=mp[s[i]].end()) nxt=*it;
           auto pt=mp[s[i]].find(j); 
           if(pt!=mp[s[i]].begin()) pt--,prev=*pt;
           if(nxt>prev) ans+=2*solve(i+1,j-1,s,mp)+2,ans%=N;
           else if(nxt==prev) ans+=2*solve(i+1,j-1,s,mp)+1,ans%=N;
           else ans+=2*solve(i+1,j-1,s,mp)-solve(nxt+1,prev-1,s,mp),ans%=N;
        }
        return dp[i][j]=ans;
    }
    int countPalindromicSubsequences(string s) {
        int n=s.size();
        map<char,set<int>> mp;
        for(int i=0;i<n;i++)mp[s[i]].insert(i);
        memset(dp,-1,sizeof(dp));
        return (solve(0,n-1,s,mp)+N)%N;
    }
};
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