Split in Three

#include <bits/stdc++.h>
#include <climits>

using namespace std;

template<class T>
using V = vector<T>;
template<class T>
using VV = V<V<T>>;

using ld = long double;
#define ll long long
using ull = unsigned ll;
using PLL = pair<ll, ll>;
using VLL = V<ll>;
using VB = V<bool>;
using VVB = VV<bool>;
using VVLL = VV<ll>;
using Gr = VVLL;
using MLL = map<ll, ll>;
#define UMLL unordered_map<ll, ll, custom_hash>

//using int128 = __int128;
//using double128 = __float128;

#define fast ios_base::sync_with_stdio(0); cin.tie(nullptr); cout.tie(nullptr); cerr.tie(nullptr);

#define INF LONG_MAX
#define MINF LONG_MIN

#define R &
#define CR const R

#define FORI(i, a, b) for(ll i = a, max##i = b; i < max##i; ++i)
#define FOR(i, n) FORI(i, 0, n)
#define RFORI(i, a, b) for(ll i = a, min##i = b; i >= min##i; --i)
#define RFOR(i, n) RFORI(i, n, 0)
#define FORA(i, a) for(auto i : a)
#define FORAR(i, a) for(auto R i : a)
#define FORACR(i, a) for(auto CR i : a)
#define ALL(obj) begin(obj), end(obj)
#define Count(q) while(q--)
#define OK cerr << "OK\n";

#define mp make_pair
#define pb push_back

//#define DEBUG

template<class T>
T sqr(T x)
{
    return x * x;
}

void YES(bool g, ostream R os, bool upper = true)
{
    if(g)
        if(upper)
            os << "YES";
        else
            os << "Yes";
    else
        if(upper)
            os << "NO";
        else
            os << "No";

    os << "\n";
}

template<class T>
void show(T CR t, ostream R os = cerr)
{
    FORACR(i, t)
        os << i << " ";
    os << "\n";
}

template<class T>
void show2d(T CR t, ostream R os = cerr)
{
    FORACR(i, t)
        show(i, os);
    os << "\n";
}

constexpr ll MOD = 1e9 + 7;
//constexpr ll len = 2e5 + 100;

constexpr ld PI = atanl(1.0L) * 4;

struct custom_hash
{
    static uint64_t splitmix64(uint64_t x)
    {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator() (uint64_t x) const
    {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

//arr
void init() {}

void solve(istream R is, ostream R os)
{
    ll n;
    is >> n;

    ll t = n * (n + 1) / 2;
    if(t % 3)
    {
        os << "IMPOSSIBLE\n";
        return;
    }

    ll s = t / 3 - 1; //s; s + 1; s + 2
    cerr << s << "\n";

    VLL a(3, 0);

    VLL res(n);

    RFOR(i, n - 1)
    {
        FOR(j, 3)
            if(a[j] + i + 1 <= s + j)
            {
                a[j] += i + 1;
                res[i] = j + 1;

                break;
            }
    }

    show(res, os);
}

void tester(istream R is, ostream R os)
{
    fast
    init();
    ll q = 1;
    //is >> q;
    os << setprecision(999);

    Count(q)
        solve(is, os);
}

int main()
{
    //ifstream in("input.txt");
    //ofstream out("output.txt");

    tester(cin, cout);
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

1

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

4

Test 4

Group: 1, 2

Verdict: ACCEPTED

6

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

11

Test 7

Group: 1, 2

Verdict: ACCEPTED

14

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: ACCEPTED

300

Test 10

Group: 2

Verdict: ACCEPTED

1519

Test 11

Group: 2

Verdict: ACCEPTED

1551

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

1616

Test 14

Group: 2

Verdict: ACCEPTED

1649

Test 15

Group: 2

Verdict: ACCEPTED