In the realm of Enchanted Isles, the Gates of Harmony guard the entrance to the ethereal sanctuary of music. To unlock these gates and access the symphonic realms within, travelers must possess a sacred harmony code, meticulously validated through celestial harmonies. The validation process unfolds with intricate patterns to ensure only those in tune with the cosmic melodies may enter the sanctuary. The validation mechanism is outlined as follows: Sum the digits at celestial positions from left to right, where celestial positions are those whose indices are prime numbers. Compute the product of the digits at mystical positions from right to left, where mystical positions are those whose indices are multiples of 3. Determine if the absolute difference between the results from step 1 and step 2 is a prime number. If it is, the harmony code is considered valid; otherwise, it is invalid. Example 1: Consider the harmony code 864201379. Step 1. Sum the digits at celestial positions: 6 + 4+0+7=17 Step 2. Compute the product of the digits at mystical positions: 9*4 = 36 Step 3. Determine if the absolute difference between the results from step 1 and step 2 is prime: 117-36) 19 (prime). Result: The harmony code 864201379 is valid. Example 2: Now, let's examine the harmony code 135792468. Step 1. Sum the digits at celestial positions: 1+7+4=12 Step 2. Compute the product of the digits at mystical positions: 8 * 2 = 16 Step 3. Determine if the absolute difference between the results from step 1 and step 2 is prime: 112-161 = 4 (not prime) Result: The harmony code 135792468 is invalid. Example 3: Finally, let's check the harmony code 246813579. Step 1. Sum the digits at celestial positions: 2 +6+1+5=14 Step 2. Compute the product of the digits at mystical positions: 9*8 = 72 Step 3. Determine if the absolute difference between the results from step 1 and step 2 is a prime number: 114-721 = 58 (not prime) Result: The harmony code 246813579 is invalid. Your task is to develop a program that validates these sacred harmony codes. The program should prompt the user to input harmony codes one at a time. After each input, it should determine the validity of the harmony code based on the validation steps described above. Valid harmony codes should be stored in one array, and invalid harmony codes should be stored in another. The program should continue accepting harmony codes until the user enters O, at which point it should display the valid and invalid harmony codes arrays and terminate. Please provide the specified program structure and problem scenario, adhering to the given guidelines and examples

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In the realm of Enchanted Isles, the Gates of Harmony guard the entrance to the
ethereal sanctuary of music. To unlock these gates and access the symphonic realms
within, travelers must possess a sacred harmony code, meticulously validated
through celestial harmonies. The validation process unfolds with intricate patterns to
ensure only those in tune with the cosmic melodies may enter the sanctuary.
The validation mechanism is outlined as follows:
Sum the digits at celestial positions from left to right, where celestial positions are
those whose indices are prime numbers.
Compute the product of the digits at mystical positions from right to left, where
mystical positions are those whose indices are multiples of 3.
Determine if the absolute difference between the results from step 1 and step 2 is a
prime number. If it is, the harmony code is considered valid; otherwise, it is invalid.
Example 1:
Consider the harmony code 864201379.
Step 1. Sum the digits at celestial positions: 6 + 4+0+7=17
Step 2. Compute the product of the digits at mystical positions: 9 * 4 = 36
Step 3. Determine if the absolute difference between the results from step 1 and step
2 is prime: 117-361 = 19 (prime)
Result: The harmony code 864201379 is valid.
Example 2:
Now, let's examine the harmony code 135792468.
Step 1. Sum the digits at celestial positions: 1+7+4=12
Step 2. Compute the product of the digits at mystical positions: 8 * 2 = 16
Step 3. Determine if the absolute difference between the results from step 1 and step
2 is prime: |12-161 = 4 (not prime)
Result: The harmony code 135792468 is invalid.
Example 3:
Finally, let's check the harmony code 246813579.
Step 1. Sum the digits at celestial positions: 2 +6+1+5=14
Step 2. Compute the product of the digits at mystical positions: 9*8 = 72
Step 3. Determine if the absolute difference between the results from step 1 and step
2 is a prime number: 114 -721 = 58 (not prime)
Result: The harmony code 246813579 is invalid.
Your task is to develop a program that validates these sacred harmony codes. The
program should prompt the user to input harmony codes one at a time. After each
input, it should determine the validity of the harmony code based on the validation
steps described above. Valid harmony codes should be stored in one array, and
invalid harmony codes should be stored in another. The program should continue
accepting harmony codes until the user enters O, at which point it should display the
valid and invalid harmony codes arrays and terminate.
Please provide the specified program structure and problem scenario, adhering to
the given guidelines and examples
Transcribed Image Text:In the realm of Enchanted Isles, the Gates of Harmony guard the entrance to the ethereal sanctuary of music. To unlock these gates and access the symphonic realms within, travelers must possess a sacred harmony code, meticulously validated through celestial harmonies. The validation process unfolds with intricate patterns to ensure only those in tune with the cosmic melodies may enter the sanctuary. The validation mechanism is outlined as follows: Sum the digits at celestial positions from left to right, where celestial positions are those whose indices are prime numbers. Compute the product of the digits at mystical positions from right to left, where mystical positions are those whose indices are multiples of 3. Determine if the absolute difference between the results from step 1 and step 2 is a prime number. If it is, the harmony code is considered valid; otherwise, it is invalid. Example 1: Consider the harmony code 864201379. Step 1. Sum the digits at celestial positions: 6 + 4+0+7=17 Step 2. Compute the product of the digits at mystical positions: 9 * 4 = 36 Step 3. Determine if the absolute difference between the results from step 1 and step 2 is prime: 117-361 = 19 (prime) Result: The harmony code 864201379 is valid. Example 2: Now, let's examine the harmony code 135792468. Step 1. Sum the digits at celestial positions: 1+7+4=12 Step 2. Compute the product of the digits at mystical positions: 8 * 2 = 16 Step 3. Determine if the absolute difference between the results from step 1 and step 2 is prime: |12-161 = 4 (not prime) Result: The harmony code 135792468 is invalid. Example 3: Finally, let's check the harmony code 246813579. Step 1. Sum the digits at celestial positions: 2 +6+1+5=14 Step 2. Compute the product of the digits at mystical positions: 9*8 = 72 Step 3. Determine if the absolute difference between the results from step 1 and step 2 is a prime number: 114 -721 = 58 (not prime) Result: The harmony code 246813579 is invalid. Your task is to develop a program that validates these sacred harmony codes. The program should prompt the user to input harmony codes one at a time. After each input, it should determine the validity of the harmony code based on the validation steps described above. Valid harmony codes should be stored in one array, and invalid harmony codes should be stored in another. The program should continue accepting harmony codes until the user enters O, at which point it should display the valid and invalid harmony codes arrays and terminate. Please provide the specified program structure and problem scenario, adhering to the given guidelines and examples
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