Number of Ways to Wear Different Hats to Each Other
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 i^th 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
1There is only one way to choose hats given the conditions: the first person chooses hat 3, the second person chooses hat 4, and the last one chooses hat 5.
Example 2
Input
hats = [[3,5,1],[3,5]]Output
4There are 4 ways to choose hats: (3,5), (5,3), (1,3), and (1,5).
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.