#include<iostream>
#include<sstream>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<string>
#include<stack>
#include<queue>
#include<deque>
#include<set>
#include<map>
#include<algorithm>
#include<functional>
#include<utility>
#include<cmath>
#include<complex>
#include<iomanip>

using namespace std;

#define REP(i,s,e) for(int i=int(s);i<=int(e);i++)
#define rep(i,n) for(int i=0;i<int(n);i++)
#define pi 3.14159265358979

int main(void){

	int n;
	for(;;){
	cin >> n;
	if(n==0) break;

	int s=0;
	for(int i=1;i*i<=n;i++){
	if(n%i==0){
	if(n==i*i) s+=i;
	else s+=i+n/i;
	}
	}

	s-=n;
	if(s<n) cout << "deficient number" << endl;
	if(s==n) cout << "perfect number" << endl;
	if(s>n) cout << "abundant number" << endl;

	}

	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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<sstream>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<string>
#include<stack>
#include<queue>
#include<deque>
#include<set>
#include<map>
#include<algorithm>
#include<functional>
#include<utility>
#include<cmath>
#include<complex>
#include<iomanip>

using namespace std;

#define REP(i,s,e) for(int i=int(s);i<=int(e);i++)
#define rep(i,n) for(int i=0;i<int(n);i++)
#define pi 3.14159265358979

int main(void){

	int n;
	for(;;){
	cin >> n;
	if(n==0) break;

	int s=0;
	for(int i=1;i*i<=n;i++){
	if(n%i==0){
	if(n==i*i) s+=i;
	else s+=i+n/i;
	}
	}

	s-=n;
	if(s<n) cout << "deficient number" << endl;
	if(s==n) cout << "perfect number" << endl;
	if(s>n) cout << "abundant number" << endl;

	}

	return 0;
}
```