human
Solve in Python:
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.
 ... Write me a the Python program you requested?
assistant
#Here is the Python program you requested.

class Solution:
    def numberWays(self, hats: List[List[int]]) -> int:
        tot=len(hats)
        h=[[False]*tot for i in range(41)]
        for i in range(len(hats)):
            for j in range(len(hats[i])):
                h[hats[i][j]][i]=True
        
        f=[[0]*(1<<tot) for i in range(41)]
        f[0][0] = 1
        mod=10**9+7
        for i in range(41):
            for j in range(1<<tot):
                f[i][j] = (f[i][j] + f[i - 1][j])%mod
                for k in range(tot):
                    if (j & (1 << k))!=0 and h[i][k]:
                        f[i][j] = (f[i][j] + f[i - 1][j ^ (1 << k)]) % mod
        return f[40][(1 << tot) - 1]