# 0793. Preimage Size of Factorial Zeroes Function

https://leetcode.com/problems/preimage-size-of-factorial-zeroes-function

## Description

Let `f(x)` be the number of zeroes at the end of `x!`. Recall that `x! = 1 * 2 * 3 * ... * x` and by convention, `0! = 1`.

* For example, `f(3) = 0` because `3! = 6` has no zeroes at the end, while `f(11) = 2` because `11! = 39916800` has two zeroes at the end.

Given an integer `k`, return the number of non-negative integers `x` have the property that `f(x) = k`.

**Example 1:**

```
**Input:** k = 0
**Output:** 5
**Explanation:** 0!, 1!, 2!, 3!, and 4! end with k = 0 zeroes.
```

**Example 2:**

```
**Input:** k = 5
**Output:** 0
**Explanation:** There is no x such that x! ends in k = 5 zeroes.
```

**Example 3:**

```
**Input:** k = 3
**Output:** 5
```

**Constraints:**

* `0 <= k <= 109`

## ac

```java
```
