#include<iostream>
#include<iomanip>
#include<algorithm>
#include<bitset>
#include<cctype>
#include<climits>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<deque>
#include<list>
#include<map>
#include<set>
#include<stack>
#include<string>
#include<sstream>
#include<queue>
#include<vector>
using namespace std;

int main(void) {
	while (true) {
		int n; cin >> n;
		if (n == 0)break;


		int s = 0;	s -= n;
		for (int i = 1; i <= sqrt(n); i++) {
			if (n%i == 0) {
				s += n / i;
				if (n != 1 && i != n / i) s += i;
			}
		}
		//cout << s << endl;

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

	}
	return 0;
}
### Prompt

Your challenge is to write 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<iomanip>
#include<algorithm>
#include<bitset>
#include<cctype>
#include<climits>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<deque>
#include<list>
#include<map>
#include<set>
#include<stack>
#include<string>
#include<sstream>
#include<queue>
#include<vector>
using namespace std;

int main(void) {
	while (true) {
		int n; cin >> n;
		if (n == 0)break;


		int s = 0;	s -= n;
		for (int i = 1; i <= sqrt(n); i++) {
			if (n%i == 0) {
				s += n / i;
				if (n != 1 && i != n / i) s += i;
			}
		}
		//cout << s << endl;

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

	}
	return 0;
}
```