Farmer John has four fields of soybeans planted. Farmer John has decided to put in a new, more efficient irrigation system to water his soybean crops. His estimate is that the new system will cost about $35,000. Soybeans are going for about $8.87 a bushel. John knows that over a growing season soybeans will use 9 inches of water and produce 65 bushels per acre. He knows that there are roughly 27,000 gallons of water in an acre-inch, and that irrigation water will cost about $1.50 per 1000 gallons. He also knows that an acre is 43,560 square feet. A square acre is about 208.7 ft. x 208.7 ft. He wonders: How many bushels does he need to produce to pay for the water system and the water used this year? How many acres of land will that require? As he ponders on these problems, he sketches a map of his soybean fields that shows how the irrigation system will cover the crops. This is shown in the image above. The square ABCD has it's vertices located at the centers of four identical circles, which are the regions covered by the new circular irrigation system. Farmer John is intrigued by the pattern shown in the shaded region of the map, and wonders further 3. What is the area of the shaded region? 4. What is the length of one side of the smallest square ABCD large enough to pay his costs? His problem is that the shaded region and other areas outside the circles will not produce any crops if it's not watered, so he won't make any money on them. We can write a program that would calculate these numbers for him directly, but John is thinking about it from another perspective. He wants to know for a given distance between A and B: How many acres would be watered in the circles? How many bushels would be produced? What would be the size of that shaded middle region in acres? How much of a profit or loss would he get? Write a program that takes as user input the distance AB, and answers these questions. Example output is below, but your code should work for any inputs, not just these specific ones. You are required to provide test cases for one valid input and one invalid input in your main code. Your program should not crash.