1434 - Number of Ways to Wear Different Hats to Each Other\.

Hard

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

Given a 2D integer array hats, where hats[i] is a list of all hats preferred by the <code>i^th</code> 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 <code>10⁹ + 7</code>.

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.

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.