# 1922. Count Good Numbers

https://leetcode.com/problems/count-good-numbers

## Description

A digit string is **good** if the digits **(0-indexed)** at **even** indices are **even** and the digits at **odd** indices are **prime** (`2`, `3`, `5`, or `7`).

* For example, `"2582"` is good because the digits (`2` and `8`) at even positions are even and the digits (`5` and `2`) at odd positions are prime. However, `"3245"` is **not** good because `3` is at an even index but is not even.

Given an integer `n`, return _the **total** number of good digit strings of length_ `n`. Since the answer may be large, **return it modulo** `109 + 7`.

A **digit string** is a string consisting of digits `0` through `9` that may contain leading zeros.

**Example 1:**

```
**Input:** n = 1
**Output:** 5
**Explanation:** The good numbers of length 1 are "0", "2", "4", "6", "8".
```

**Example 2:**

```
**Input:** n = 4
**Output:** 400
```

**Example 3:**

```
**Input:** n = 50
**Output:** 564908303
```

**Constraints:**

* `1 <= n <= 1015`

## ac

```java
```
