Problem:
Score : 500 points

Problem Statement

Snuke received a positive integer N from Takahashi.
A positive integer m is called a favorite number when the following condition is satisfied:

The quotient and remainder of N divided by m are equal, that is, \lfloor \frac{N}{m} \rfloor = N \bmod m holds.

Find all favorite numbers and print the sum of those.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

8

Sample Output 1

10

There are two favorite numbers: 3 and 7. Print the sum of these, 10.

Sample Input 2

1000000000000

Sample Output 2

2499686339916

Watch out for overflow.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pb push_back
#define rep(i, s, n) for (int i = s; i < n; i++)
#define rrep(i, s, n) for (int i = (n)-1; i >= (s); i--)
#define all(a) a.begin(),a.end()
typedef pair<int,int>pint;
typedef vector<int>vint;
typedef vector<pint>vpint;
const long long MOD = 1000000007, INF = 1e17;
template<class T>inline bool chmax(T& a,T b){if(a<b){a=b;return true;}return false;}
template<class T>inline bool chmin(T& a,T b){if(a>b){a=b;return true;}return false;}
//******************************************************************************
template<typename T>vector<T>
make_v(size_t a){return vector<T>(a);}
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){
	return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

template<typename T,typename V>
typename enable_if<is_class<T>::value==0>::type
fill_v(T &t,const V &v){t=v;}

template<typename T,typename V>
typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t,const V &v){
	for(auto &e:t) fill_v(e,v);
}


signed main()
{
	int N;
	cin>>N;
	if(N==1){
		cout<<0<<endl;
		return 0;
	}
	int ans=0;
	for(int i=1;i*i<=N;i++){
		if((N-i)%i==0){
			int t = (N-i)/i;
			if(N/t==N%t)ans+=t;
		}
	}
	cout<<ans<<endl;
}