Split in Three

#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 105;
int sol[N];
 
int main(){
    int n;
    cin >> n;
    if(n % 3 == 1){
        cout << "IMPOSSIBLE\n";
        return 0;
    }
    int m = n;
    int q;
    while(m > 10){
        q = m - 5;
        sol[q] = 1;
        sol[q + 5] = 1;
        sol[q + 1] = 2;
        sol[q + 4] = 2;
        m -= 6;
    }
    int a = (m * 1ll * (m + 1) / 2 - 3) / 3;
    int b = a + 1;
    int j;
    int cum0 = 0, cum1 = 0;
    bool bruh=false;
    for(int i = 0 ; i < (1 << m); i ++ ){
        j = i;
        while(1){
            cum0 = 0;
            cum1 = 0;
            for(int q = 0 ; q < m ; q ++ ){
                sol[q + 1] = 0;
                if((i & (1 << q))){
                    if((j & (1 << q))){
                        cum0 += (q + 1);
                        sol[q + 1] = 1;
                    }
                    else{
                        cum1 += (q + 1);
                        sol[q + 1] = 2;
                    }
                }
                if(cum0 == a && cum1 == b){
                    bruh=true;
                    break;
                }
            }
            j = ((j - 1) & i);
            if(j == 0 || bruh) break;
        }
        if(bruh) break;
    }
    for(int i = 1; i <= n; i ++ ){
        if(sol[i] == 0){
            cout << 3 << " ";
        }
        else{
            cout << sol[i] << " ";
        }
    }
    return 0;
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

Test 4

Group: 1, 2

Verdict: ACCEPTED

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

Test 7

Group: 1, 2

Verdict: ACCEPTED

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: ACCEPTED

Test 10

Group: 2

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: ACCEPTED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

Test 14

Group: 2

Verdict: ACCEPTED

Test 15

Group: 2

Verdict: ACCEPTED