<p>Given a string <code>s</code>, return <em>the number of <strong>palindromic substrings</strong> in it</em>.</p>

<p>A string is a <strong>palindrome</strong> when it reads the same backward as forward.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within the string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;abc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Three palindromic strings: &quot;a&quot;, &quot;b&quot;, &quot;c&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aaa&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> Six palindromic strings: &quot;a&quot;, &quot;a&quot;, &quot;a&quot;, &quot;aa&quot;, &quot;aa&quot;, &quot;aaa&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

'''
memo[i][j] = memo[i][j-1] + memo[i+1][j] - memo[i+1][j-1] (+ 1 if first and last characters are the same)
return value for abcba = return value for abcb + return value for bcba + 1

memo[0][0] = 1
memo[x][x] = 1 for all x


        for i in range(0, len(s)):
            for j in range(i+1, len(s)):
                memo[i][j] = memo[i][j-1] + 1
                if j > i and is_palindrome(s[i:j+1]):
                    memo[i][j] += 1
                    print("Palindrome found at "+str((i, j))+": "+s[i:j+1]+" has "+str(memo[i][j])+" palindromic substrings")
        print(str(memo))
        return memo[0][len(s)-1]

                for x in range(0, (j - i)//2 + 1):
                    #print("Comparing "+s[i + x]+" and "+s[j - x])
                    if s[i + x] != s[j - x]:
                        #print(s[i:j+1]+" is not a palindrome, because "+s[i + x]+" != "+s[j - x])
                        p[i][j] = False
                        break
                if p[i][j] is None:
                    #print(s[i:j+1]+" is a palindrome")
                    p[i][j] = True
'''
class Solution:
    def countSubstrings(self, s: str) -> int:
        if len(s) < 2:
            return len(s)
        p = [ ([None] * len(s)) for x in range(0, len(s)) ]
        for x in range(0, len(s)):
            p[x][x] = True
        def is_palindrome(i: int, j: int) -> bool:
            #print(s[i:j+1])
            if p[i][j] is None:
                if j < i:
                    print("Error 1")
                    return False
                elif j - i == 0:
                    p[i][j] = True
                elif j - i == 1:
                    p[i][j] = s[i] == s[j]
                else:
                    p[i][j] = is_palindrome(i+1, j-1) and s[i] == s[j]
            '''if p[i][j]:
                print(s[i:j+1]+" is a palindrome")
            else:
                print(s[i:j+1]+" is NOT a palindrome")'''
            return p[i][j]
        memo = [ ([1] * len(s)) for x in range(0, len(s)) ]
        for i in range(len(s) - 1, -1, -1):
            for j in range(i+1, len(s)):
                if j - i == 0:
                    memo[i][j] = 1
                    continue
                elif j - i == 1:
                    if s[i] != s[j]:
                        memo[i][j] = 2
                    else:
                        memo[i][j] = 3
                    continue
                memo[i][j] = memo[i+1][j] + memo[i][j-1]- memo[i+1][j-1]
                #answer = self.countSubstrings(s[1:]) + self.countSubstrings(s[:len(s) - 1]) - self.countSubstrings(s[1:len(s)-1])
                if is_palindrome(i, j):
                    memo[i][j] += 1
                #print("3: String \""+s[i:j+1]+"\" has "+str(memo[i][j])+" palindromic substrings")
        #print(str(memo))
        return memo[0][len(s)-1]
66611