More than 2500 years ago, mathematicians got interested in numbers. Armstrong Numbers: The number 153 has the odd property that 1'+5+3= 1 + 125+27 153 Namely, 153 is equal to the sum of the cubes of its own digits. Perfect Numbers: A number is said to be perfect if it is the sum of its own divisors (excluding itself). For example, 6 is perfect since 1, 2, and 3 divide evenly into 6 and 1+2+3=6. Input File The input is taken from a file named number.in and which a sequence of numbers, one perline, terminated by a line containing the number 0. Output File A file number.out which contains all the the number read from the input file. These numbers are printed one perline followed by a sentence indicating whether the number is or is not armstrong number and whether it is nor not a perfect number. Sample Input 153 0 Sample Output 153 is an Armstrong number but it is not a perfect number. 6 is not an Armstrong number but it is a perfect number.

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