<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 memo[1001][1001][4];
class Solution {
public:
	string S;
	int MOD = 1000000007;

	int dp(int start,int end,int alpha){
		//base case
		if(start>end)return 0;
		if(start==end){
			if(S[start] == (alpha+'a') )return 1;
			return 0;
		}
		
		if(memo[start][end][alpha]!=-1)return memo[start][end][alpha];
		
		int dev=0;
		if(S[start]==S[end] && S[start]==(alpha+'a')){
			dev=2;
			for(int i=0;i<4;i++)
				dev=(dev + dp(start+1,end-1,i) )%MOD;
		}else{
			dev= (dev + dp(start,end-1,alpha))%MOD;
			dev= (dev + dp(start+1,end,alpha))%MOD;
			dev= (dev - dp(start+1,end-1,alpha))%MOD;
			if(dev<0)dev+=MOD;
		}
		
		memo[start][end][alpha]=dev;
		return dev;
	}
	
	int countPalindromicSubsequences(string _S) {
		S=_S;
		memset(memo,-1,sizeof(memo));
		int ans=0;
		
		for(int i=0;i<4;i++)
			ans= (ans + dp(0, S.size()-1, i))%MOD;
		
		return ans;        
	}
};
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