Write the following program using C++ or Java or Python, which ever you prefer.

Write a program that helps an interactive user search for "near misses" of the form (x, y, z, n, k) in the formula xn + yn = z", where x, y, z, n, k are positive integers, where 2 10. You may want to impose an upper limit on k if you find that your program is crashing due to overflowing integer variables, but don't make it TOO small, or you will limit the kinds of near misses you can find. Your program should then look for "near misses of the form x + yn z. A "near miss" is a RELATIVELY small difference between (x + yn) and za for some integers x, y, and z. Your program should systematically search for x, y, and z combinations that are "almost right." NOTE WELL: Fermat's last theorem tells us that there should NOT be any x + y = z" combinations that are EXACTLY right for any n > 2. Also notice that although x and y are constrained above, z is NOT constrained directly. For each possible x,y combination, I suggest that you calculate (x + yn), and then look for whole numbers z and z + 1 that "bracket" (x + yn), so that z" 10. You may want to impose an upper limit on k if you find that your program is crashing due to overflowing integer variables, but don't make it TOO small, or you will limit the kinds of near misses you can find. Your program should then look for "near misses of the form x + yn z. A "near miss" is a RELATIVELY small difference between (x + yn) and za for some integers x, y, and z. Your program should systematically search for x, y, and z combinations that are "almost right." NOTE WELL: Fermat's last theorem tells us that there should NOT be any x + y = z" combinations that are EXACTLY right for any n > 2. Also notice that although x and y are constrained above, z is NOT constrained directly. For each possible x,y combination, I suggest that you calculate (x + yn), and then look for whole numbers z and z + 1 that "bracket" (x + yn), so that z"