Number of Ways to Wear Different Hats to Each Other
There are n people and 40 types of hats labeled from 1 to 40.
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 ith person.
Return the number of ways that n people can wear different hats from 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.
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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