Kolmijako

#include <bits/stdc++.h>

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

void print_sum(int a, int b, int e, int e2 = 0, int e3 = 0) {
    for (int i = a; i <= b; ++i) {
        if (i != e && i != e2 && i != e3) {
            std::cout << i << ' ';
        }
    }
    if (e < a && e > 0) std::cout << e << ' ';
    if (e2 < a && e2 > 0) std::cout << e2;
    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) {
            int i = n;
            const auto [s1i, s1e] = make_sum(S3, i);
            auto [s2i, s2e] = make_sum(S3, s1i - 1, s1e);
            if (s1e == s2e && s1e <= 2) {
                std::cout << "NO\n";
                continue;
            }
            int s2e2 = 0;
            if (s1e == s2e) {
                s2e = s2e - 1;
                s2e2 = 1;
            }
            std::cout << "YES\n";
            std::cout << ((i - s1i + 1) + (s1e > 0)) << '\n';
            print_sum(s1i, i, s1e);
            std::cout << ((s1i - s2i) + (s2e > 0) + (s2e2 > 0) - (s1e > 0 && s1e >= s2i)) << '\n';
            print_sum(s2i, s1i - 1, s2e, s2e2, s1e);
            std::cout << ((s2i - 1) - (s1e > 0) - (s2e > 0) - (s2e2 > 0)) << '\n';
            print_sum(1, s2i - 1, s1e, s2e, s2e2);
        } else {
            std::cout << "NO\n";
        }
    }
}

Test 1

Group: 1, 2, 3

Verdict: WRONG ANSWER

Test 2

Group: 2, 3

Verdict: WRONG ANSWER

Test 3

Group: 3

Verdict: WRONG ANSWER