Split in Three

#include <bits/stdc++.h>

using namespace std;

#define int long long
#define ff first
#define ss second
#define pb push_back

const int N = 2e5 + 5, inf = 1e18 + 100;

int u[105];

signed main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;

    int s = n * (n + 1) / 2;
    if (s % 3) return cout << "IMPOSSIBLE", 0;

    int x = s / 3 - 1, ok = 0;
    for (int i = n; i >= 1; --i)
    {
        if (ok) break;
        for (int j = 1; j <= n; ++j)
        {
            if (i == j || u[i] > 0 || u[j] > 0) continue;
            if (i + j == x) {ok = 1, u[i] = u[j] = 1; break;}
            if (i == x) {ok = 1, u[i] = 1; break;}
            if (j == x) {ok = 1, u[j] = 1; break;}
        }
    }

    ok = 0;
    for (int i = n; i >= 1; --i)
    {
        if (ok) break;
        for (int j = 1; j <= n; ++j)
        {
            if (i == j || u[i] > 0 || u[j] > 0) continue;
            if (i + j == x + 1) {ok = 1, u[i] = u[j] = 2; break;}
            if (i == x + 1) {ok = 1, u[i] = 2; break;}
            if (j == x + 1) {ok = 1, u[j] = 2; break;}
        }
    }

    for (int i = 1; i <= n; ++i)
        cout << (!u[i] ? 3 : u[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: WRONG ANSWER

Test 10

Group: 2

Verdict: WRONG ANSWER

Test 11

Group: 2

Verdict: WRONG ANSWER

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: WRONG ANSWER

Test 14

Group: 2

Verdict: WRONG ANSWER

Test 15

Group: 2

Verdict: ACCEPTED