# Factorial Sum

Given a positive integer `n`

, return whether `n`

can be written as the sum of distinct positive factorial numbers.

**Constraints**

`0 < n < 2 ** 31`

https://binarysearch.com/problems/Factorial-Sum

## Examples

### Example 1

**Input**

- n =
`31`

**Output**

- answer =
`True`

**Explanation**

Since `31 = 4! + 3! + 1!`

### Example 2

**Input**

- n =
`4`

**Output**

- answer =
`False`

**Explanation**

Since `4 = 2! + 2!`

but not distinct.

### Example 3

**Input**

- n =
`6`

**Output**

- answer =
`True`

### Example 4

**Input**

- n =
`29`

**Output**

- answer =
`False`

## Leave a comment