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g1901_2000.s1922_count_good_numbers.readme.md Maven / Gradle / Ivy

1922\. Count Good Numbers

Medium

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