Split in Three

#include<bits/stdc++.h>
#define ll long long
#define inf 1e17
using namespace std;

void solve(){
    ll n;
    cin >> n;
    vector<ll> v(n + 1);
    ll val = n * (n + 1) / 2;
    if(val % 3){
        cout << "IMPOSSIBLE";
        return;
    }
    val = val / 3;
    val++;
    ll sum = 0;
    for(int i = n; i >= 1; i--){
        if(sum + i > val){
            ll need = val - sum;
            if(need >= 3){
                v[need] = 3;
                break;
            }
            if(need == 2){
                v[i - 1] = 3;
                v[3] = 3;
                break;
            }
            v[i - 2] = 3;
            v[3] = 3;
            break;
        }
        sum += i;
        v[i] = 3;
        if(sum == val){
            break;
        }
    }
    val--;
    sum = 0;
    for(int i = n; i >= 1; i--){
        if(v[i]){
            continue;
        }
        if(sum + i > val){
            ll need = val - sum;
            if(v[need]){
                v[1] = 2;
                v[need - 1] = 2;
            }
            else{
                v[need] = 2;
            }
            break;
        }
        sum += i;
        v[i] = 2;
        if(sum == val){
            break;
        }
    }
    for(int i = 1; i <= n; i++){
        if(v[i] == 0){
            v[i] = 1;
        }
        cout << v[i] << " ";
    }
}
int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    int t = 1;
    //cin >> t;
    while(t--){
        solve();
    }
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: WRONG ANSWER

Test 4

Group: 1, 2

Verdict: WRONG ANSWER

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