P15930 [TOPC 2021] Aliquot Sum

A divisor of a positive integer $n$ is an integer $d$ where $m = \frac{n}{d}$ 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 examples, $s(12) = 1 + 2 + 3 + 4 + 6 = 16$, $s(21) = 1 + 3 + 7 = 11$, 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 intewer $y$ 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. Please write a program to classify them.

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

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

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