#include <iostream>
#include <vector>

using namespace std;

const int PERFECT = 0;
const int ABUNDANT = 1;
const int DEFICIENT = 2;

int classifyNumber(int n, vector<int> &factors);
vector<int> factorNumber(int n);
int sumOfVector(vector<int> v);
void printVector(vector<int> v);

int main (int argc, char * const argv[]) {
	int n;
	vector<int> factors;
	
	cout << "\n\nNew Horizons Governors School Team B\n";
	cout << "Enter a positive integer to classify: ";
	cin >> n;
	
	if (n <= 0)
		return -1;
	
	
	int classification = classifyNumber(n, factors);
	cout << "This number is ";
	if (classification == PERFECT)
		cout << "perfect";
	else if (classification == ABUNDANT)
		cout << "abundant";
	else if (classification == DEFICIENT)
		cout << "deficient";
	else
		cout << "something went terribly wrong";
	
	cout << "\nFactors are given below\n";
	printVector(factors);
	cout << "\n";
	
    return 0;
}

int classifyNumber(int n, vector<int> &factors) {
	factors = factorNumber(n);
	int factorSum = sumOfVector(factors);
	
	if (factorSum == n)
		return PERFECT;
	else if (factorSum > n)
		return ABUNDANT;
	else
		return DEFICIENT;
}

vector<int> factorNumber(int n) {
	vector<int> v;
	v.push_back(1); //one is always a factor
	
	for (int i = 2; i < n; i++)
		if (n % i == 0)
			v.push_back(i);
	return v;
}
int sumOfVector(vector<int> v) {
	int sum = 0;
	for (vector<int>::iterator it = v.begin(); it != v.end(); it++)
		sum += *it;
	
	return sum;
}

void printVector(vector<int> v) {
	for (vector<int>::iterator it = v.begin(); it != v.end(); it++)
		cout << *it << " ";
}