Sum

#include <iostream>
#include <set>

int main (){
    std::set<std::string> koik;
    int S;
    std::cin >> S;
    for (int i=1;i<S/3;i++){ // 1..S/3
        for (int u=1;u<S/2;u++){ // 1..S/2
            if (i!=u){
            for (int o=S/3;o<S;o++){ // S/3..S
                if (i!=o && u!=o){
                if (i+o+u==S){
                    std::string koos;
                    if (i<o){
                        if (i<u){
                            koos += std::to_string(i);
                            koos += " ";
                            if (o<u){
                                koos += std::to_string(o);
                                koos += " ";
                                koos += std::to_string(u);
                            } else {
                                koos += std::to_string(u);
                                koos += " ";
                                koos += std::to_string(o);
                            }
                        } else {
                            koos += std::to_string(u);
                            koos += " ";
                            koos += std::to_string(i);
                            koos += " ";
                            koos += std::to_string(o);
                        }
                    } else {
                        if (o<u){
                            koos += std::to_string(o);
                            koos += " ";
                            if (i<u){
                                koos += std::to_string(i);
                                koos += " ";
                                koos += std::to_string(u);
                            } else {
                                koos += std::to_string(u);
                                koos += " ";
                                koos += std::to_string(i);
                            }
                        } else {
                            koos += std::to_string(u);
                            koos += " ";
                            koos += std::to_string(o);
                            koos += " ";
                            koos += std::to_string(i);
                        }
                    }
                    //std::cout << koos << '\n';
                    koik.insert(koos);
                }
                }
            }
            }
        }
    }
    std::cout << koik.size() << '\n';
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED