An Armstrong number of n digits is an integer such that the sum of its digits each one to the power of n is equal to the number itself.

For example, $9,474$ is an Armstrong number as

All $1-$digit numbers are obviously Armstrong numbers.

Write program that reads a sequence of numbers, one number per line, from the file numbers.txt; and copies the Armstrong numbers to the new file armstrong.txt$,$ one number per line, in the same order.

For example, given this numbers.txt: