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# Aliquot Sum

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## Description:

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.

## Input:

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 $n_1,\dots,n_T$.

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

## Output:

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.

## Sample Input:

3
12 21 28


## Sample Output:

abundant
deficient
perfect


Info

Provider CodeForces Gym

Code GYM103373B

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Date 10/31/2021 14:45:58

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