Write a program to print:</p>

1. The perfect numbers between $1\,000$ and $9\,999$ inclusive. A perfect number is a positive integer which is equal to the sum of its proper divisors. A proper divisor is any divisor less than the number itself. For example, $6$ is a perfect number since $1 + 2 + 3 = 6$.
2. All integers between $100$ and $999$ inclusive which are equal to the sum of the cubes of their digits.

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출력 형식

All the perfect numbers between $1\,000$ and $9\,999$ inclusive on one line, followed by all integers between $100$ and $999$ inclusive which are equal to the sum of the cubes of their digits on one line.