Count Five-Position Palindromes in a Digit String
Company: Visa
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Other
### Problem
Count subsequences of digit string `s` with exactly five characters that form a palindrome. Different increasing choices of indices count separately, even when their resulting strings are identical. Return the count modulo `10^9 + 7`.
```cpp
class Solution {
public:
int countPalindromes(string s);
};
```
### Examples
**Example 1:**
```text
Input: s = "111111"
Output: 6
Explanation: Omitting any one of the six positions gives one of six index-distinct palindromic subsequences.
```
**Example 2:**
```text
Input: s = "12345"
Output: 0
Explanation: The only length-five subsequence is not a palindrome.
```
### Constraints
- `1 <= s.length <= 10000`.
- s consists of decimal digits.
### Clarifying Questions
- Must the five positions be consecutive? No; they form a subsequence.
- Do equal strings from different indices count separately? Yes.
- Is the length exactly five? Yes.
- What if the input has fewer than five characters? Return 0.
```hint Check the boundary
Distinguish the number of different strings from the number of different five-index choices.
```
Overview: Count five-position palindromic subsequences in a digit string, counting different index selections separately and reducing modulo 1,000,000,007.