#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <complex>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cmath>
#include <queue>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
const int INF = 1<<29;

int main() {
  int n;
  while(cin >> n,n) {
    if (n==1)      {
      cout << "deficient number" << endl;
      continue;
    }
    int hoge = 1;
    for (int i=2; i*i<=n; ++i) {
      if (n%i==0) {
        if (i*i!=n)
          hoge += i+n/i;
        else
          hoge += i;
      }
    }
    if (hoge<n) {
      cout << "deficient number" << endl;
    }else if (hoge==n)
      cout << "perfect number" << endl;
    else
      cout << "abundant number" << endl;
  }
}
### Prompt

Create a solution in Cpp for 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 <cstdio>
#include <vector>
#include <algorithm>
#include <complex>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cmath>
#include <queue>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
const int INF = 1<<29;

int main() {
  int n;
  while(cin >> n,n) {
    if (n==1)      {
      cout << "deficient number" << endl;
      continue;
    }
    int hoge = 1;
    for (int i=2; i*i<=n; ++i) {
      if (n%i==0) {
        if (i*i!=n)
          hoge += i+n/i;
        else
          hoge += i;
      }
    }
    if (hoge<n) {
      cout << "deficient number" << endl;
    }else if (hoge==n)
      cout << "perfect number" << endl;
    else
      cout << "abundant number" << endl;
  }
}
```