You are given a map of the Roman Empire. There are N + 1 cities (numbered from 0 to N) and N directed roads between them. The road network is connected; that is, ignoring the directions of roads, there is a route between each pair of cities. The capital of the Roman Empire is Rome. We know that all roads lead to Rome. This means that there is a route from each city to Rome. Your task is to find Rome on the map, or decide that it is not there. The roads are described by two arrays A and B of N integers each. For each integer K (0 <= K < N), there exists a road from city A[K] to city B[K]. Write a function: function solution(A, B); that, given two arrays A and B, returns the number of the city which is Rome (the city that can be reached from all other cities). If no such city exists, your function should return -1. Examples: 1. Given A = [1,2,3] and B = [0,0,0], the function should return 0. Rome has the number 0 on the map. 2. Given A = [0,1,2,4,5] and B = [2,3,3,3,2], the function should return 3. Rome has the number 3 on the map. From cities 1,2 and 4, there is a direct road to city 3. From cities 0 and 5, the roads to city 3 go through city 2.3. Given A = [2,3,3,4] and B = [1,1,0,0], the function should return -1. There is no Rome on the map. Write an efficient algorithm for the following assumptions: • N is an integer within the range [1...200,000]; • each element of arrays A, B is an integer within the range [0...N]; • the road network is connected