please give an algorithm using priority queues that has a running time of O(n+mlogm).

1 Problem Definition You are a house painter that is available from day 1n (inclusive). You can only paint one house in a day. It also only takes one day to paint a house. You are given m houses. For each house i, you are also given startDay and endDay i for i=1,,m. The house i can only be painted on a day between startDay i and endDay i (inclusive). The given houses are already sorted primarily on startDay and secondarily on endDay (in case of equality of the startDay). You are tasked to find the maximum number of houses that you can paint. 2 Greedy Strategies For each of the following greedy strategies, you must i) design a O(n+mlog(m)) algorithm; ii) provide an instance where the strategy yields an optimal solution; iii) provide an instance where the strategy does not yield an optimal solution or prove that it is an optimal strategy. Your algorithm for Strat1 must have a (n) running time. The remaining strategies must have a (n+mlog(m)) running time. Strat1 Iterate over each day starting from day 1n. For each day, among the unpainted houses that are available to be painted on that day, paint the house that started being available the earliest. Strat2 Iterate over each day starting from day 1n. For each day, among the unpainted houses that are available that day, paint the house that started being available the latest. Strat3 Iterate over each day starting from day 1n. For each day, among the unpainted houses that are available that day, paint the house that is available for the shortest duration. Strat4 Iterate over each day starting from day 1n. For each day, among the unpainted houses that are available that day, paint the house that will stop being available the earliest. Hint:- While iterating over each day, maintain a priority queue that contains the unpainted houses that are available to be painted on the current day