Idea is start from each index and try to extend palindrome for both odd and even length.

```
public class Solution {
int count = 0;
public int countSubstrings(String s) {
if (s == null || s.length() == 0) return 0;
for (int i = 0; i < s.length(); i++) { // i is the mid point
extendPalindrome(s, i, i); // odd length;
extendPalindrome(s, i, i + 1); // even length
}
return count;
}
private void extendPalindrome(String s, int left, int right) {
while (left >=0 && right < s.length() && s.charAt(left) == s.charAt(right)) {
count++; left--; right++;
}
}
}
```