Number of Ways to Wear Different Hats to Each Other

Problem: Number of Ways to Wear Different Hats to Each Other There are n people numbered from 0 to n - 1. There are multiple hats, each represented by a positive integer. Person i is willing to wear only hats in hats[i]. Return the number of valid assignments such that: Each person wears exactly one hat. No two people wear the same hat. Person i wears a hat from hats[i]. Return the answer modulo 10^9 + 7. The interview mentioned that the constraints were smaller than the original LeetCode problem, so brute force/backtracking might be acceptable. The constraints below are for the standard version. Input Format n k0 h00 h01 ... k1 h10 h11 ... ... kn-1 ... For each person i, the first integer ki is the number of hats they like, followed by ki hat IDs. Output Format Print one integer: the number of valid assignments. Constraints 1 <= n <= 10 1 <= hats[i].length <= 40 1 <= hats[i][j] <= 40 Each person's list has no duplicate hats. Example Input 3 2 3 4 2 4 5 1 5 Output 1