p01224 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
```python
def f(p):
    ans=1
    if p<=5: return 0
    for n in range(2,int(p**0.5)+1):
        if p%n==0:
            if n!=p//n:ans+=n+p//n
            else:ans+=n
    return ans

while 1:
    n=int(input())
    if n==0:break
    m=f(n)
    if n==m:print('perfect number')
    else: print('deficient number' if n>m else 'abundant number')
```