Aliquot Sum

A divisor of a positive integer $n$ is an integer $d$ such that $m = \frac{n}{d}$ is an integer. In this problem, we define the aliquot sum $s(n)$ of a positive integer $n$ as the sum of all divisors of $n$ other than $n$ itself. For example, $s(12) = 1 + 2 + 3 + 4 + 6 = 16$, $s(21) = 1 + 3 + 7 = 11$, and $s(28) = 1 + 2 + 4 + 7 + 14 = 28$.

With the aliquot sum, we can classify positive integers into three types: abundant numbers, deficient numbers, and perfect numbers. The rules are as follows.

1. A positive integer $x$ is an abundant number if $s(x) > x$.
2. A positive integer $y$ is a deficient number if $s(y) < y$.
3. A positive integer $z$ is a perfect number if $s(z) = z$.

You are given a list of positive integers. Write a program to classify them.

The first line of the input contains one positive integer $T$, the number of test cases. The second line contains $T$ space-separated positive integers $n_1, \dots, n_T$.

Output $T$ lines. If $n_i$ is an abundant number, print abundant on the $i$-th line. If $n_i$ is a deficient number, print deficient on the $i$-th line. If $n_i$ is a perfect number, print perfect on the $i$-th line.

• $1 \le T \le 10^6$
• $1 \le n_i \le 10^6$ for $i \in \{1, 2, \dots, T\}$.