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
import java.util.Scanner;
public class Main
{
	public static void main(String arg[])
	{
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext())
		{
			int n=sc.nextInt();
			if(n==0)
				return;
			if(n==1)
			{
				System.out.println("deficient number");
				continue;
			}
			
			int sum=1;			
			for(int i=2;i*i<n;i++)
			{
				if(n%i==0)
				{
					sum+=i+n/i;
					if(i==n/i)
						sum-=i;
				}
				if(sum>n)
				{
					System.out.println("abundant number");
					break;
				}
			}
			if(n==sum)
				System.out.println("perfect number");
			else if(n>sum)
				System.out.println("deficient number");
		}
	}
}