In the distant future, the Interstellar Navigation Control System relies on a sophisticated set of criteria to evaluate navigational coordinates for space probes. The navigation validation process involves intricate spatial calculations and cosmic mathematics. The validation mechanism is described as follows: Calculate the Galactic Sum: • Sum the values of the coordinates at odd dimensions (e.g., x, y, z) from the origin. Compute the Celestial Product: • Take the product of the values at even dimensions (e.g., x, y. z) from the origin. Determine Cosmic Harmony: • If the absolute difference between the Galactic Sum and the Celestial Product is a prime number, the coordinates are considered valid for navigation; otherwise, they are deemed invalid. Example 1: Consider the coordinates (3, 7, 12). Galactic Sum: 3 + 12 = 15 Celestial Product: 7*1=7 -Absolute Difference: [15-71-8 (not prime) Coordinates (3, 7, 12) are invalid. Example 2: Now, let's examine the coordinates (5, 2, 9). Galactic Sum: 5+9=14 Celestial Product: 2*1 =2 -Absolute Difference: [14-21 = 12 (not prime) Coordinates (5,2, 9) are invalid. Example 3: Finally, let's check the coordinates (8, 6, 3). Galactic Sum: 8+3=11 - Celestial Product: 6*1=6 -Absolute Difference: 111-61-5 (prime) Coordinates (8, 6, 3) are valid. Your task is to write a program that reads sets of coordinates from user input and classifies them as "valid" or "invalid." The program should have two arrays for valid and invalid coordinates, initially empty. The array sizes should be set to 15, assuming the user will enter at most 15 sets of coordinates. The program should start asking for a set of coordinates (three integers) from the user. If the coordinates are valid according to the validation steps, they should be added to the "valid coordinates" array. If the coordinates are invalid, they should be added to the "invalid coordinates" array. If the user enters the coordinates (0, 0, 0), the program should display the valid and invalid coordinates arrays and stop. Error handling for non-integer inputs is not required.