# 1434. Number of Ways to Wear Different Hats to Each Other

<https://leetcode.com/problems/number-of-ways-to-wear-different-hats-to-each-other>

## Description

There are `n` people and 40 types of hats labeled from 1 to 40.

Given a list of list of integers `hats`, where `hats[i]` is a list of all hats preferred by the `i-th` person.

Return the number of ways that the n people wear different hats to each other.

Since the answer may be too large, return it modulo `10^9 + 7`.

**Example 1:**

```

**Input:** hats = [[3,4],[4,5],[5]]
**Output:** 1
**Explanation:** There is only one way to choose hats given the conditions. 
First person choose hat 3, Second person choose hat 4 and last one hat 5.
```

**Example 2:**

```

**Input:** hats = [[3,5,1],[3,5]]
**Output:** 4
**Explanation:** There are 4 ways to choose hats
(3,5), (5,3), (1,3) and (1,5)
```

**Example 3:**

```

**Input:** hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]
**Output:** 24
**Explanation:** Each person can choose hats labeled from 1 to 4.
Number of Permutations of (1,2,3,4) = 24.
```

**Example 4:**

```

**Input:** hats = [[1,2,3],[2,3,5,6],[1,3,7,9],[1,8,9],[2,5,7]]
**Output:** 111
```

**Constraints:**

* `n == hats.length`
* `1 <= n <= 10`
* `1 <= hats[i].length <= 40`
* `1 <= hats[i][j] <= 40`
* `hats[i]` contains a list of **unique** integers.

## ac

```java
```