#include<iostream>
#include<string>
#include<algorithm>
#include<map>
#include<set>
#include<utility>
#include<vector>
#include<cmath>
#include<cstdio>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define pb push_back
#define mp make_pair
#define it ::iterator
#define all(in) in.begin(),in.end()
const double PI=acos(-1);
const double ESP=1e-10;
using namespace std;
int main(){
  long long int in;
  while(cin>>in,in){
    long long int sum=0;
    double tmp=sqrt(in);
    int co;
    if(tmp-(int)tmp!=0.0)co=(int)tmp+1;
    else co=(int)tmp+2;
    loop(i,1,co)if(in%i==0){
      if(in!=i*i)sum+=in/i+i;
      else sum+=i;
    }
    sum-=in;
    if(sum==in)cout<<"perfect number"<<endl;
    else if(sum<in)cout<<"deficient number"<<endl;
    else cout<<"abundant number"<<endl;
  }


}
### Prompt

Your task is to create a cpp solution to the following problem:

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

### Response

```cpp
#include<iostream>
#include<string>
#include<algorithm>
#include<map>
#include<set>
#include<utility>
#include<vector>
#include<cmath>
#include<cstdio>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define pb push_back
#define mp make_pair
#define it ::iterator
#define all(in) in.begin(),in.end()
const double PI=acos(-1);
const double ESP=1e-10;
using namespace std;
int main(){
  long long int in;
  while(cin>>in,in){
    long long int sum=0;
    double tmp=sqrt(in);
    int co;
    if(tmp-(int)tmp!=0.0)co=(int)tmp+1;
    else co=(int)tmp+2;
    loop(i,1,co)if(in%i==0){
      if(in!=i*i)sum+=in/i+i;
      else sum+=i;
    }
    sum-=in;
    if(sum==in)cout<<"perfect number"<<endl;
    else if(sum<in)cout<<"deficient number"<<endl;
    else cout<<"abundant number"<<endl;
  }


}
```