p-norms are mathematical distance functions with interesting properties and applications. The most well-known 3 norms are the 1-norm, 2-norm, and infinity norms, and they are defined, below. The 2-norm is simply the Euclidean distance. It is the shortest distance possible between two points. However, some real life applications makes it impossible to use the 2-norm. For example, a Robot that wants to move in a room that has obsticales (tables, chairs, furniture,.. etc) can not use the 2-norm distance metric. Instead, it will use the 1-norm distance which allows the Robot to go around room objects. The same is true for a human or robot taxi cab that will have to go around the building blocks. This is the reason why the 1-norm distance metric is often called the "Taxi cab distance". The distance is computed using the sum of all distances travelled around the city block, or room objects if used inside a room. The infinity-norm computes the maximum of absolute values, given a number of values. For example, the infinity norm of this set of numbers: (-6, 3, 4) is 6. The infinity-norm for 2 points that have 2 dimensions, x and y, is simply the largest distance in either x or y dimensions, as shown in the equations, below. In other words, for a robot that is travelling around a long building, the infinity-norm tells us which distance is larger, the length (x) or width (y) of the building. Write Python code for the 3 norm distances, for 2 points in the plane, using the equations below. Your input values should be converted to float (no need to validate the float input). Your code should use input validation for the 3 norm names, as shown in the sample runs. Use the sample runs, below to guide your program output.