#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define all(a) (a).begin(), (a).end() #define rep(i, n) for (ll i = 0; i < (n); i++) #define req(i, a, b) for (ll i = (a); i < (b); i++) #define pb push_back #define debug(x) cerr << __LINE__ << ' ' << #x << ':' << (x) << '\n' #define debug2(x, y) cerr << __LINE__ << ' ' << #x << ':' << (x) << ',' << #y << ':' << (y) << '\n' #define debug3(x, y, z) cerr << __LINE__ << ' ' << #x << ':' << (x) << ',' << #y << ':' << (y) << ',' << #z << ':' << (z) << '\n' using namespace std; typedef long long ll; typedef unsigned int uint; typedef unsigned long long ull; typedef long double ld; template using P = pair; template using pri_l = priority_queue; template using pri_s = priority_queue, greater>; constexpr int inf = 1000000010; constexpr int inf2 = 2000000010; constexpr ll INF = 1000000000000000010; constexpr ll INF4 = 4000000000000000010; constexpr int mod1e9 = 1000000007; constexpr int mod998 = 998244353; constexpr ld eps = 1e-12; constexpr ld pi = 3.141592653589793238; constexpr ll ten(int n) { return n ? 10 * ten(n - 1) : 1; }; int dx[] = { 1,0,-1,0,1,1,-1,-1,0 }; int dy[] = { 0,1,0,-1,1,-1,1,-1,0 }; ll mul(ll a, ll b) { return (b != 0 && a > INF / b ? INF : a * b); } void fail() { cout << "-1\n"; exit(0); } void no() { cout << "No\n"; exit(0); } template void er(T a) { cout << a << '\n'; exit(0); } template inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return true; } return false; } template istream& operator >>(istream& s, vector& v) { for (auto& e : v) s >> e; return s; } template ostream& operator <<(ostream& s, const vector& v) { for (auto& e : v) s << e << ' '; return s; } template ostream& operator << (ostream& s, const pair& p) { s << p.first << ' ' << p.second; return s; } struct fastio { fastio() { cin.tie(0); cout.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(20); } }fastio_; namespace rdv { random_device seed_gen; mt19937_64 engine(seed_gen()); ll rnum(ll r) { return engine() % r; } // [0, r) ll rnum(ll l, ll r) { return rnum(r - l) + l; } // [l, r) ll rng(ll l, ll r) { return rnum(l, r + 1); } // [l, r] double rng01() { return engine() * pow(2, -64); } template void shuf(vector& v) { shuffle(all(v), engine); } void shuf(string& s) { shuffle(all(s), engine); } } using namespace rdv; template vector compress(vector v) { int n = v.size(); vector tmp = v; sort(tmp.begin(), tmp.end()); tmp.erase(unique(tmp.begin(), tmp.end()), tmp.end()); vector res(n); for (int i = 0; i < n; i++) res[i] = lower_bound(tmp.begin(), tmp.end(), v[i]) - tmp.begin(); return res; } #include using namespace atcoder; constexpr ll mod = mod998; using mint = static_modint; istream& operator >>(istream& s, mint& m) { ll y; s >> y; m = y; return s; } ostream& operator <<(ostream& s, mint& m) { return s << m.val(); } ostream& operator <<(ostream& s, const vector& v) { for (auto& e : v) s << e.val() << ' '; return s; } vector fac, inv, facinv; void modcalc(int n) { fac.resize(n); inv.resize(n); facinv.resize(n); fac[0] = 1; fac[1] = 1; inv[1] = 1; facinv[0] = 1; facinv[1] = 1; for (ll i = 2; i < n; i++) { fac[i] = fac[i - 1] * i; inv[i] = -inv[mod % i] * (mod / i); facinv[i] = facinv[i - 1] * inv[i]; } } mint comb(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[k] * facinv[n - k]; } mint perm(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[n - k]; } mint hom(ll n, ll k) { if (n < 0 || k < 0 || n == 0 && k > 0) return 0; if (n == 0 && k == 0) return 1; return fac[n + k - 1] * facinv[k] * facinv[n - 1]; } int main() { bool DEBUG = false; int N = DEBUG ? 30 : 300; int TEST = 1; cin >> TEST; while (TEST--) { vector> a(4); rep(i, 4) { if (DEBUG) { while (1) { a[i].first = rng(10, 20); a[i].second = rng(10, 20); bool good = true; rep(j, i) { if (a[i].first == a[j].first) good = false; if (a[i].second == a[j].second) good = false; } if (good) break; } // a = { {6,9},{7,6},{5,7},{8,5} }; } else { cin >> a[i].first >> a[i].second; a[i].first += N / 2; a[i].second += N / 2; } } rep(i, 4) rep(j, i) { assert(a[i].first != a[j].first); assert(a[i].second != a[j].second); } if ((a[0].first + a[0].second + a[1].first + a[1].second) % 2 == 1) { // パリティが合ってないと一生合わない cout << "-1\n"; continue; } if (a[0].first > a[1].first) { swap(a[0], a[1]); swap(a[2], a[3]); } if (a[0].second + 1 == a[1].second) { int x = a[0].first - N / 2, y = a[0].second - N / 2; if (!DEBUG) { cout << 5 << '\n'; cout << x - 1 << ' ' << y << '\n'; cout << x << ' ' << y - 1 << '\n'; cout << x + 1 << ' ' << y << '\n'; cout << x + 1 << ' ' << y + 2 << '\n'; cout << x + 2 << ' ' << y + 1 << '\n'; } continue; } if (a[0].second - 1 == a[1].second) { int x = a[0].first - N / 2, y = a[0].second - N / 2; if (!DEBUG) { cout << 5 << '\n'; cout << x - 1 << ' ' << y << '\n'; cout << x << ' ' << y - 1 << '\n'; cout << x << ' ' << y + 1 << '\n'; cout << x + 1 << ' ' << y - 2 << '\n'; cout << x + 2 << ' ' << y - 1 << '\n'; } continue; } int alx = -1, aly = -1; auto bfs = [&](int sx, int sy, int gx, int gy, vector>& v) -> int { vector D(N + 3, vector(N + 3, inf)); D[sx + 1][sy + 1] = 0; queue> que; que.push({ sx, sy }); while (!que.empty()) { auto [x, y] = que.front(); que.pop(); rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (0 <= nx + 1 && nx <= N + 1 && 0 <= ny + 1 && ny <= N + 1 && (nx == -1 or ny == -1 or nx == N + 1 or ny == N + 1 or v[nx][ny] != -1) && D[nx + 1][ny + 1] == inf) { bool bad = false; if (nx != alx or ny != aly) rep(i, 4) if (a[i].first == nx && a[i].second == ny) bad = true; if (!bad) { D[nx + 1][ny + 1] = D[x + 1][y + 1] + 1; que.push({ nx, ny }); } } } } return D[gx + 1][gy + 1]; }; if (DEBUG) rep(i, 4) debug(a[i]); vector> ans; // Alice を x = 1, Bob を x = N - 1 に持っていく vector v(N + 1, vector(N + 1)); // use : 1, ng : -1 rep(i, 4) v[a[i].first][a[i].second] = 1; // rollback dfs auto sol = [&](bool is_Alice) -> vector> { vector> path; bool fin = false; if (is_Alice) path = { a[0] }; else path = { a[1] }; auto dfs = [&](auto dfs, int x, int y, int px, int py, bool is_Alice) -> void { if (x == (is_Alice ? 1 : N - 1)) fin = true; if (fin) return; vector> cand; // debug2(x, y); P prior = { -1, -1 }; rep(d, 4) { bool bad = false; int nx = x + dx[d], ny = y + dy[d]; if (ny <= 5 or ny >= N - 5) continue; rep(i, 4) if (nx == a[i].first && ny == a[i].second) bad = true; if (bad) continue; if (v[nx][ny] == 1) continue; if (v[nx][ny] == -1) continue; if (nx == px && ny == py) continue; if (!is_Alice) if (abs(nx - a[0].first) + abs(ny - a[0].second) <= 1) continue; if (is_Alice) if (abs(nx - a[1].first) + abs(ny - a[1].second) <= 1) continue; if (is_Alice) { if (abs(nx - a[2].first) + abs(ny - a[2].second) <= 1) continue; if (abs(nx - a[3].first) + abs(ny - a[3].second) == 1) { prior = { nx, ny }; } } if (!is_Alice) { if (abs(nx - a[3].first) + abs(ny - a[3].second) <= 1) continue; if (abs(nx - a[2].first) + abs(ny - a[2].second) == 1) { prior = { nx, ny }; } } cand.push_back({ nx, ny }); } sort(all(cand), [&](P p0, P p1) { if (p0 == prior) return true; if (p1 == prior) return false; return is_Alice ? (p0 < p1) : (p0 > p1); }); for (auto& [nx, ny] : cand) { path.push_back({ nx, ny }); v[nx][ny] = 1; dfs(dfs, nx, ny, x, y, is_Alice); if (fin) break; path.pop_back(); v[nx][ny] = 0; } }; if (is_Alice) dfs(dfs, a[0].first, a[0].second, -1, -1, true); else dfs(dfs, a[1].first, a[1].second, -1, -1, false); return path; }; auto p0 = sol(1); int s0 = ssize(p0); rep(i, s0 - 1) { auto& [x, y] = p0[i]; rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (v[nx][ny] == 0) v[nx][ny] = -1; } } for (auto& [x, y] : p0) v[x][y] = 0; // if (DEBUG) debug(p0); auto p1 = sol(0); int s1 = ssize(p1); rep(i, s1 - 1) { auto& [x, y] = p1[i]; rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (v[nx][ny] == 0) v[nx][ny] = -1; } } for (auto& [x, y] : p0) v[x][y] = 1; // if (DEBUG) debug(p1); int y0 = p0.back().second, y1 = p1.back().second; auto q0 = p0, q1 = p1; // debug(1); int d0 = bfs(a[0].first, a[0].second, p0.back().first, p0.back().second, v); int d1 = bfs(a[1].first, a[1].second, p1.back().first, p1.back().second, v); // debug2(p0, p1); // debug2(d0, d1); // debug(ssize(p0)); while (d0 < d1) { auto& [x, y] = p0.back(); if (x == N - 1) p0.push_back({ x, y + 1 }); else if (y == 1) p0.push_back({ x + 1, y }); else p0.push_back({ x, y - 1 }); d0++; } while (d0 > d1) { auto& [x, y] = p1.back(); if (x == 1) p1.push_back({ x, y + 1 }); else if (y == 1) p1.push_back({ x - 1, y }); else p1.push_back({ x, y - 1 }); d1++; } // debug(p0.back()); debug(p1.back()); while (p0.back() != p1.back()) { auto& [x0, y0] = p0.back(); auto& [x1, y1] = p1.back(); if (x0 == N - 1) p0.push_back({ x0, y0 + 1 }); else if (y0 == 1) p0.push_back({ x0 + 1, y0 }); else p0.push_back({ x0, y0 - 1 }); if (x1 == 1) p1.push_back({ x1, y1 + 1 }); else if (y1 == 1) p1.push_back({ x1 - 1, y1 }); else p1.push_back({ x1, y1 - 1 }); } int X = p0.back().first, Y = p0.back().second; bool upd = false; if (X == 1 && Y == 1) upd = true; if (X == 1 && Y == 2) upd = true; if (X == 2 && Y == 1) upd = true; if (X == N - 1 && Y == 1) upd = true; if (X == N - 2 && Y == 1) upd = true; if (X == N - 1 && Y == 2) upd = true; // debug2(X, Y); if (upd) { rep(_, 3) q0.pop_back(); auto [xb, yb] = q0.back(); q0.push_back({ xb, yb + 1 }); q0.push_back({ xb, yb + 2 }); q0.push_back({ xb, yb + 3 }); q0.push_back({ xb - 1, yb + 3 }); q0.push_back({ xb - 2, yb + 3 }); q0.push_back({ xb - 2, yb + 2 }); q0.push_back({ xb - 2, yb + 1 }); q0.push_back({ xb - 2, yb }); q0.push_back({ xb - 3, yb }); p0 = q0, p1 = q1; // debug(ssize(p0)); // for (auto &[x, y] : p0) debug2(x, y); rep(i, N + 1) rep(j, N + 1) v[i][j] = 0; rep(i, ssize(p0)) v[p0[i].first][p0[i].second] = 1; rep(i, ssize(p1)) v[p1[i].first][p1[i].second] = 1; rep(i, ssize(p0) - 1) { auto& [x, y] = p0[i]; rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (v[nx][ny] == 0) v[nx][ny] = -1; } } rep(i, ssize(p1) - 1) { auto& [x, y] = p1[i]; rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (v[nx][ny] == 0) v[nx][ny] = -1; } } d0 = bfs(a[0].first, a[0].second, p0.back().first, p0.back().second, v); d1 = bfs(a[1].first, a[1].second, p1.back().first, p1.back().second, v); // debug2(d0, d1); while (d0 < d1) { auto& [x, y] = p0.back(); if (x == N - 1) p0.push_back({ x, y + 1 }); else if (y == 1) p0.push_back({ x + 1, y }); else p0.push_back({ x, y - 1 }); d0++; } while (d0 > d1) { auto& [x, y] = p1.back(); if (x == 1) p1.push_back({ x, y + 1 }); else if (y == 1) p1.push_back({ x - 1, y }); else p1.push_back({ x, y - 1 }); d1++; } // debug(p0.back()); debug(p1.back()); while (p0.back() != p1.back()) { auto& [x0, y0] = p0.back(); auto& [x1, y1] = p1.back(); if (x0 == N - 1) p0.push_back({ x0, y0 + 1 }); else if (y0 == 1) p0.push_back({ x0 + 1, y0 }); else p0.push_back({ x0, y0 - 1 }); if (x1 == 1) p1.push_back({ x1, y1 + 1 }); else if (y1 == 1) p1.push_back({ x1 - 1, y1 }); else p1.push_back({ x1, y1 - 1 }); } X = p0.back().first, Y = p0.back().second; // debug2(X, Y); // debug2(d0, d1); bool upd = false; if (X == 1 && Y == 1) upd = true; if (X == 1 && Y == 2) upd = true; if (X == 2 && Y == 1) upd = true; if (X == N - 1 && Y == 1) upd = true; if (X == N - 2 && Y == 1) upd = true; if (X == N - 1 && Y == 2) upd = true; assert(!upd); } rep(i, ssize(p0)) v[p0[i].first][p0[i].second] = 1; rep(i, ssize(p1)) v[p1[i].first][p1[i].second] = 1; rep(i, ssize(p0) - 1) { auto& [x, y] = p0[i]; // debug2(x, y); rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (v[nx][ny] == 0) v[nx][ny] = -1; } } rep(i, ssize(p1) - 1) { auto& [x, y] = p1[i]; // debug2(x, y); rep(d, 4) { int nx = x + dx[d], ny = y + dy[d]; if (v[nx][ny] == 0) v[nx][ny] = -1; } } rep(i, N + 1) rep(j, N + 1) if (v[i][j] == -1) ans.push_back({ i - N / 2, j - N / 2 }); if (DEBUG) { vector C(N + 1, vector(N + 1, '.')); rep(i, N + 1) rep(j, N + 1) if (v[i][j] == -1) C[i][j] = 'X'; rep(i, 4) { // assert(C[a[i].first][a[i].second] == '.'); C[a[i].first][a[i].second] = 'A' + i; } assert(X == p1.back().first); assert(Y == p1.back().second); int D0 = bfs(a[0].first, a[0].second, X, Y, v); int D1 = bfs(a[1].first, a[1].second, X, Y, v); alx = a[2].first, aly = a[2].second; int D2 = bfs(a[0].first, a[0].second, a[2].first, a[2].second, v); alx = a[3].first, aly = a[3].second; int D3 = bfs(a[1].first, a[1].second, a[3].first, a[3].second, v); rep(i, N + 1) { rep(j, N + 1) cerr << C[i][j]; cerr << '\n'; } debug2(D0, D1); debug2(D2, D3); assert(D0 == D1); assert(D0 < D2); assert(D1 < D3); assert(D2 != inf); assert(D3 != inf); } else { int sz = ssize(ans); assert(sz <= 4000); cout << sz << '\n'; for (auto& [x, y] : ans) cout << x << ' ' << y << '\n'; } } }