Kolmijako

#include <bits/stdc++.h>

std::pair<int, int> make_sum(int S, int n, int e = 0) {
    for (int s = 0; s != S; --n) {
        if (n == e) {
            continue;
        }
        if (s + n <= S) {
            s += n;
        } else {
            return {n + 1, S - s};
        }
    }
    return {n + 1, 0};
}

void print_range(int a, int b, int e = 0, int e2 = 0, int e3 = 0) {
    for (int i = a; i <= b; ++i) {
        if (i == e || i == e2 || i == e3) {
            continue;
        }
        std::cout << i << ' ';
    }
    std::cout << '\n';
}

int main() {
    int t;
    std::cin >> t;
    for (int i = 0, n; i < t; ++i) {
        std::cin >> n;
        int S = n * (n + 1) / 2;
        int S3 = S / 3;
        if (S % 3 == 0 && S3 >= n) {
            const auto [s1i, s1e] = make_sum(S3, n);
            auto [s2i, s2e] = make_sum(S3, s1i - 1, s1e);

            const auto s1s = n - s1i + 1 + (s1e > 0);
            std::cout << "YES\n";
            std::cout << s1s << '\n';
            if (s1e) std::cout << s1e << ' ';
            print_range(s1i, n);
            if (s1e && s1e == s2e) {
                int s2e1 = (s2e == 1) ? 2 : 1;
                int s2e2 = (s2e == 1) ? s2i - 1 : s1e - 1;
                s2i += (s2e == 1);
                const auto s2s = s1i - s2i + 2;
                const auto s3s = n - s1s - s2s;
                std::cout << s2s << '\n';
                std::cout << s2e1 << ' ' << s2e2 << ' ';
                print_range(s2i, s1i - 1);
                std::cout << s3s << '\n';
                print_range(1, s2i - 1, s1e, s2e1, s2e2);

            } else {
                const auto s2s = s1i - s2i + (s2e > 0) - (s1e > s2i);
                const auto s3s = n - s1s - s2s;
                std::cout << s2s << '\n';
                if (s2e) std::cout << s2e << ' ';
                print_range(s2i, s1i - 1, s1e);
                std::cout << s3s << '\n';
                print_range(1, s2i - 1, s1e, s2e);
            }
        } else {
            std::cout << "NO\n";
        }
    }
}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 2, 3

Verdict: WRONG ANSWER

Test 3

Group: 3

Verdict: ACCEPTED