Cross-Number Puzzle

문제

Write a program to print:

1. The perfect numbers between $10001\backslash ,000$ and $99999\backslash ,999$ 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, $66$ is a perfect number since $1+2+3=61\; +\; 2\; +\; 3\; =\; 6$.
2. All integers between $100100$ and $999999$ inclusive which are equal to the sum of the cubes of their digits.

입력

There is no input.

출력

All the perfect numbers between $10001\backslash ,000$ and $99999\backslash ,999$ inclusive on one line, followed by all integers between $100100$ and $999999$ inclusive which are equal to the sum of the cubes of their digits on one line.