Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
//#include <atcoder/all>
using namespace std;
//using namespace atcoder;
#define ll long long
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rep1(i, n) FOR(i, 1, n+1)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i)
#define whole(x) (x).begin(),(x).end()
#define rwhole(x) (x).rbegin(), (x).rend()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define P pair<int, int>
#define debug(var) cerr << "[" << #var << "] " << var << '\n'
template<typename T1, typename T2>
bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
template<typename T1, typename T2>
bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
#define vi vector<int>
#define vl vector<ll>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define pr(s) cout << (s) << '\n'
const ll mod = 1000000007;
const int dx[] = {-1,0,1,0};
const int dy[] = {0,-1,0,1};
const int INF = 1001001001;
const ll INFll = 1E+18;


int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    ll N;
    cin >> N;
    ll w = 0;
    P p;
    bool ok = false;
    rep1(n, 3500) {
        rep(h, 3500) {
            ll x = 4*h*n-N*n-N*h;
            ll y = N*h*n;
            if (x<=0) continue;
            if (y%x!=0) continue;
            w = y/x;
            if (w>3500) continue;
            debug(w);
            p = P(n, h);
            ok = true;
            break;
        }
        if (ok) break;
    }
    debug(w);
    
    printf("%lld %lld %lld\n", p.fi, p.se, w);
    return 0;
}