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.