Perfect Number

Let S be the sum of divisors of an integer N excluding the number itself. When N = S, N is called a perfect number, when N> S, N is called a defendant number, and when N <S, N is called an abundant number. Create a program that determines whether a given integer is a perfect number, a missing number, or an abundant number.

Be careful not to exceed the program execution time.

Input

The input consists of a sequence of datasets. The number of datasets is 100 or less.

Each dataset consists of one row containing only the integer N (0 <N ≤ 100000000).

After the last dataset, there is a line marked 0 that marks the end of the input.

Output

For each dataset, print the string " perfect number "if the integer N is a perfect number," deficient number" if it is a missing number, or " abundant number "if it is an abundant number. ..

Example

Input

1 2 3 4 6 12 16 28 33550336 99999998 99999999 100000000 0

Output

deficient number deficient number deficient number deficient number perfect number abundant number deficient number perfect number perfect number deficient number deficient number abundant number

inputFormat

Input

The input consists of a sequence of datasets. The number of datasets is 100 or less.

Each dataset consists of one row containing only the integer N (0 <N ≤ 100000000).

After the last dataset, there is a line marked 0 that marks the end of the input.

outputFormat

Output

For each dataset, print the string " perfect number "if the integer N is a perfect number," deficient number" if it is a missing number, or " abundant number "if it is an abundant number. ..

Example

Input

1 2 3 4 6 12 16 28 33550336 99999998 99999999 100000000 0

Output

deficient number deficient number deficient number deficient number perfect number abundant number deficient number perfect number perfect number deficient number deficient number abundant number

样例

1
2
3
4
6
12
16
28
33550336
99999998
99999999
100000000
0

deficient number
deficient number
deficient number
deficient number
perfect number
abundant number
deficient number
perfect number
perfect number
deficient number
deficient number
abundant number

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