// L素数が本質なのはすぐ分かるが、そこからが苦手。 // このテーブルを眺めていたら、aが素数のとき、a=m+n, m=n+1が見えた。 // https://mathlandscape.com/pythagoras-triple-table/ #include #include #include #include #include #include #include #include #include #include #include #include //#include #define rep(i, n) for(i = 0; i < n; i++) #define int long long using namespace std; //using namespace atcoder; // https://algo-method.com/tasks/553/editorial // Miller-Rabin 素数判定法 template T pow_mod(T A, T N, T M) { T res = 1 % M; A %= M; while (N) { if (N & 1) res = (res * A) % M; A = (A * A) % M; N >>= 1; } return res; } bool is_prime(long long N) { if (N <= 1) return false; if (N == 2 || N == 3) return true; if (N % 2 == 0) return false; vector A = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; long long s = 0, d = N - 1; while (d % 2 == 0) { ++s; d >>= 1; } for (auto a : A) { if (a % N == 0) return true; long long t, x = pow_mod<__int128_t>(a, d, N); if (x != 1) { for (t = 0; t < s; ++t) { if (x == N - 1) break; x = __int128_t(x) * x % N; } if (t == s) return false; } } return true; } // Pollard のロー法 long long gcd(long long A, long long B) { A = abs(A), B = abs(B); if (B == 0) return A; else return gcd(B, A % B); } long long pollard(long long N) { if (N % 2 == 0) return 2; if (is_prime(N)) return N; long long step = 0; auto f = [&](long long x) -> long long { return (__int128_t(x) * x + step) % N; }; while (true) { ++step; long long x = step, y = f(x); while (true) { long long p = gcd(y - x + N, N); if (p == 0 || p == N) break; if (p != 1) return p; x = f(x); y = f(f(y)); } } } vector prime_factorize(long long N) { if (N == 1) return {}; long long p = pollard(N); if (p == N) return {p}; vector left = prime_factorize(p); vector right = prime_factorize(N / p); left.insert(left.end(), right.begin(), right.end()); sort(left.begin(), left.end()); return left; } void solve(int L) { if (L % 4 == 0) { cout << (L / 4) * 3 << " " << (L / 4) * 4 << " " << (L / 4) * 5 << endl; return; } vector ps = prime_factorize(L); int p = ps.back(); int m = (p + 1) / 2, n = p / 2; int bai = L / p; cout << (m * m - n * n) * bai << " " << (m * m + n * n) * bai << " " << 2 * m * n * bai << endl; } signed main() { int T; cin >> T; while (T--) { int L; cin >> L; solve(L); } return 0; }