Problem Description

Takahashi loves perfect things.

Among natural numbers, there are what we call perfect numbers. A perfect number is a natural number whose sum of divisors excluding itself equals itself. For example, in the case of $6$, $1 + 2 + 3 = 6$, so it is a perfect number. On the other hand, if the sum of divisors excluding itself is less than the number, it is called a deficient number, and if it is greater, it is called an abundant number.

Takahashi is interested in a particular natural number. Please determine whether it is a perfect number, a deficient number, or an abundant number for him.

Input Format

The input is given from the standard input in the following format:

$ N $

• The first line contains the natural number $ N $ ( $1 \leq N \leq 10^{10}$ ) that Takahashi is interested in.

Output Format

Output Perfect if $ N $ is a perfect number, Deficient if it is a deficient number, and Abundant if it is an abundant number, in one line.

Sample Input and Output

Sample Input #1

6

Sample Output #1

Perfect

Sample Input #2

24

Sample Output #2

Abundant

Sample Input #3

27

Sample Output #3

Deficient

Sample Input #4

945

Sample Output #4

Abundant

Notes/Hints

Partial Points

This problem has partial points.

• If you correctly solve the dataset where $1 \leq N \leq 10^5$, you will be awarded $ 50 $ points.
• If you correctly solve the dataset where $1 \leq N \leq 10^{10}$, you will be awarded an additional $ 50 $ points. The total is $ 100 $ points.

Sample Explanation 1

Since $ 1 + 2 + 3 = 6 $, $ 6 $ is a perfect number.

Sample Explanation 2

Since $ 1 + 2 + 3 + 4 + 6 + 8 + 12 > 24 $, $ 24 $ is an abundant number.

Sample Explanation 3

Since $ 1 + 3 + 9 < 27 $, $ 27 $ is a deficient number.

见题面 Input 部分

见题面 Output 部分