#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>

using namespace std;

#define rep(i,j) REP((i), 0, (j))
#define REP(i,j,k) for(int i=(j);(i)<(k);++i)
#define between(a,x,b) ((a)<=(x)&&(x)<=(b))
#define F first
#define S second
#define INF 1 << 30

int main(){
  int N;
  while(scanf("%d", &N) && N){
    int r = sqrt(N);
    int sum = 0;
    for(int i = 1; i <= r; i++){
      if(i == N) continue;
      if(N%i == 0){
	sum += i;
	if(N/i == N || N/i == i) continue;
	sum += N/i;
      }
    }

    if(sum == N) puts("perfect number");
    else if(sum < N) puts("deficient number");
    else if(sum > N) puts("abundant number");
  }
  return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>

using namespace std;

#define rep(i,j) REP((i), 0, (j))
#define REP(i,j,k) for(int i=(j);(i)<(k);++i)
#define between(a,x,b) ((a)<=(x)&&(x)<=(b))
#define F first
#define S second
#define INF 1 << 30

int main(){
  int N;
  while(scanf("%d", &N) && N){
    int r = sqrt(N);
    int sum = 0;
    for(int i = 1; i <= r; i++){
      if(i == N) continue;
      if(N%i == 0){
	sum += i;
	if(N/i == N || N/i == i) continue;
	sum += N/i;
      }
    }

    if(sum == N) puts("perfect number");
    else if(sum < N) puts("deficient number");
    else if(sum > N) puts("abundant number");
  }
  return 0;
}
```