Divisor Abundance Classifier

MediumNumber-TheoryDivisors6 hidden tests

A number theory hobbyist classifies positive integers by comparing them to the sum of their own proper divisors (all divisors of n except n itself).

Given n, let s be the sum of the proper divisors of n. Output:

perfect if s == n
abundant if s > n
deficient if s < n

Input format

Line 1: a single integer n.

Output format

One word: perfect, abundant, or deficient.

Constraints

1 <= n <= 10000000

Examples

Example 1

Input

Expected

perfect

Explanation

Proper divisors of 28 are 1,2,4,7,14, summing to 28, so it is perfect.

Example 2

Input

Expected

abundant

Explanation

Proper divisors of 12 are 1,2,3,4,6, summing to 16 > 12, so it is abundant.

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