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.

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