<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 {
	
string s;
int n;

const int mod = 1e9 + 7;

long long dp[1005][1005][4]; // no. of palindromic subsequences in [i ... j] starting with c  

long long solve(int i, int j, int ci) {
	if (i > j) {
		return 0; // KNOW WHAT YOU ARE CODING OR DIE ... FINISHED ..... NOT GOOGLE .. STOP CODING COMPLETELY
	}
	char c = ci + 'a';
	if (dp[i][j][ci] > -1) {
		return dp[i][j][ci];
	}
	if (i == j) {
		return dp[i][j][ci] = s[i] == c;
	}
	long long res;
	if (s[i] == c && s[j] == c) {
		res = 0;
		for (int k = 0; k < 4; k++) {
			res += solve(i + 1, j - 1, k);
			res %= mod;
		}
		res += 2;
		res %= mod;
	} else if (s[i] == c) {
		res = solve(i, j - 1, ci);
	} else if (s[j] == c) {
		res = solve(i + 1, j, ci);
	} else {
		res = solve(i + 1, j - 1, ci);
	}
	return dp[i][j][ci] = res;
}

public:
    int countPalindromicSubsequences(string s1) {
		s = s1;
		n = s.length();	
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				for (int k = 0; k < 4; k++) {
					dp[i][j][k] = -1;	
				}
			}
		}	
	    long long ans = 0;
		for (int k = 0; k < 4; k++) {
			ans += solve(0, n - 1, k);
			ans %= mod;
		}    
		return ans;
    }
};

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