Perfection

Given a positive integer, determine whether it is perfect, abundant, or deficient.

If integers satisfy $a = b \times c$, then $a$ is a multiple of $b$ and of $c$, and $b$ and $c$ are divisors of $a$. A proper divisor of a positive integer is any positive divisor other than the number itself ($1$ counts as a proper divisor; the number itself does not).

Classify a number by the sum of its proper divisors:

• PERFECT: the sum of the proper divisors equals the number itself. For example, $6 = 1 + 2 + 3$ and $28 = 1 + 2 + 4 + 7 + 14$ are perfect.
• DEFICIENT: the sum of the proper divisors is smaller than the number. For example, the proper divisors of $9$ are $1, 3$, which sum to $4$, so $9$ is deficient.
• ABUNDANT: the sum of the proper divisors is larger than the number. For example, the proper divisors of $12$ are $1, 2, 3, 4, 6$, which sum to $16$, so $12$ is abundant.

$N$ positive integers are given, separated by spaces or newlines. Each integer is at most 60,000, and $1 < N < 100$. A value of $0$ marks the end of the list ($0$ itself is not processed).

Print one line for each input integer. Each line has the form integer verdict, with a single space between the integer and the verdict. The verdict is PERFECT if the number is perfect, DEFICIENT if deficient, and ABUNDANT if abundant. Keep the same order as the input.