Problem Statement

Family Dinner Problem Description You are given an integer 'n', indicating that there are n family members labeled from 1 to n. This large family completes dinner in several rounds due to limited seating at the dining table (k seats) and prerequisite relationships between members, which may be children eating first, senior members eating first, or any other reason. You are also given an array of relations where relations[i] = [member1, member2], representing prerequisite relationships where member1 must have dinner before member2. Return the minimum number of rounds needed to have dinner for all members. Note: The value of k is equal to the smallest prime factor of n Input Format The first line of input contains an integer n. The second line of input contains an integer x (number of relations). The third line of input contains an integer k (indicate two integers required in each relation.) The next x lines of the input contain two integers. Constraints 2 <= n <= 15 0 <= relati