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:1Explanation: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:4Explanation: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:24Explanation: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.

class Solution {
public int numberWays(List<List<Integer>> hats) {
}
}