A square grid is placed over a city map. There are residential areas at the coordinates (0,1), (2,3) and (5,6). The respective populations of the three areas are 2500, 2000, and 3000. A centralized facility is being considered for either the point (4,4) or the point (4,5). Which of the two points is the better location for a centralized facility, given that we wish to minimize the total Manhattan distance traveled by the population to the facility? Justify your answer by giving the total Manhattan distance traveled by the population to each of the two possible locations.

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