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, y = s / 3 - 1;
    for (int i = n; i >= 1; --i)
    {
        if (y >= i) u[i] = 1, y -= i;
        else u[y] = 1, y = 0;
    }

    y = x + 1;
    for (int i = n; i >= 1; --i)
    {
        if (u[i]) continue;
        if (!y) break;
        if (y >= i) u[i] = 2, y -= i;
        else i = y + 1;
    }

    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: 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