Assume a Taxicab is located at the origin (0,0) in the below Grid. The hori- zontal and vertical lines in the Grid is the road on which his taxi can move. If the cab wants to move to a place, say (3,4), the distance the cab has to travel is (3 - 0) + (4 - 0) = 7 units. The distance calculated in this way is called Man- hattan distance. In general, Manhattan distance between two points (x1 , y1 ) and (x2 , y2 ) is calculated as |x2 - x1 | + |y2 - y1 |. As you must be aware, the Eucledian distance between the same two points is calculated as (x2 - x1 )2 + (y2 - y1 )2 3 Figure 1: Manhattan distance Given n points to the taxicab driver located at a position (x,y), he/she has to arrange the points in the order of increasing manhattan distance. For example, If (3,4), (5,3) and (2,2) are the points given to the cab driver who is at the postion (1,1), then the driver will output (2,2), (3,4) and (5,3) as these points are in the order of increasing distance from the Taxicab position (1,1). You are required to write a program to help the driver. The input is of the following format: * The first line will contain the position of the Taxicab. For example, the position could be ((3,0)). * Next line will contain the number of points. For your program 2 <= n <= 100 * Next n lines will contain the points with each point on a new line. After reading the input, your program should calculate Manhattan distance from the Taxicab position and arrange the points in the order of increasing Manhattan distance. Each point should be printed in a new line. If Manhattan distance is equal for two points, first output the point that has the least x co- ordinate. For Example: INPUT (2,0) 4 (3,4) 4 (0,1) (6,7) (2,3) OUTPUT (0,1) (2,3) (3,4) (6,7)
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