// いろいろ高速化 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include <bits/stdc++.h> using namespace std; // 型名の短縮 using ll = long long; using ull = unsigned long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>; using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>; using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>; using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>; using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>; using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>; template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索(昇順) #define repis(i, set) for(int i = lsb(set), bset##i = set; i >= 0; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template <class T> inline T get(T set, int i) { return (set >> i) & T(1); } // 演算子オーバーロード template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; } template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; } template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; } template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include(<atcoder/all>) #include <atcoder/all> using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif void WA() { auto start = chrono::system_clock::now(); int n; cin >> n; vi x(n), y(n); rep(i, n) cin >> x[i] >> y[i]; ++x; ++x; ++y; ++y; vvi ex(2010, vi(2010)); rep(i, n) ex[x[i]][y[i]] = 1; const vi dx = { 2, 2, -2, -2, -1, 1, -1, 1 }; const vi dy = { -1, 1, -1, 1, -2, -2, 2, 2 }; int res = INF; mt19937_64 mt((int)time(NULL)); uniform_int_distribution<int> rnd(0, 7); while (1) { unordered_map<ll, int> d; bool ok = true; rep(i, n) { int k = rnd(mt); if (ex[x[i] + dx[k]][y[i] + dy[k]]) { ok = false; break; } ll h = (x[i] + dx[k]) * (ll)INF + (y[i] + dy[k]); int dir = k / 2; if (d.count(h) && d[h] != dir) { ok = false; break; } d[h] = dir; } if (ok) chmin(res, sz(d)); auto now = chrono::system_clock::now(); auto msec = chrono::duration_cast<chrono::milliseconds>(now - start).count(); if (msec >= 1950) break; } if (res == INF) res = -1; cout << res << endl; } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); auto start = chrono::system_clock::now(); int n; cin >> n; vi x(n), y(n); rep(i, n) cin >> x[i] >> y[i]; vector<pii> xy(n); rep(i, n) xy[i] = { x[i], y[i] }; sort(all(xy)); rep(i, n) tie(x[i], y[i]) = xy[i]; rep(i, n) { x[i] += 4; y[i] += 4; } constexpr int W = 1010; int ex[W][W]; rep(i, W) rep(j, W) ex[i][j] = -2; rep(i, n) ex[x[i]][y[i]] = -1; constexpr int dx[8] = {2, 2, -2, -2, -1, 1, -1, 1}; constexpr int dy[8] = {-1, 1, -1, 1, -2, -2, 2, 2}; int deg[W][W]; rep(i, W) rep(j, W) deg[i][j] = 0; rep(i, n) rep(k, 8) { int x2 = x[i] + dx[k]; int y2 = y[i] + dy[k]; deg[x2][y2]++; } int res = INF; int cost = 0; function<void(int)> rf = [&](int i) { // もう時間がないので強制終了. auto now = chrono::system_clock::now(); auto msec = chrono::duration_cast<chrono::milliseconds>(now - start).count(); if (msec >= 1980) { if (res == INF) res = -1; EXIT(res); } // これ以上調べても無駄なので打ち切り. if (cost >= res) return; if (i == n) { chmin(res, cost); return; } int lx = -1, ly = -1, lk = -1; rep(k, 8) { int x2 = x[i] + dx[k]; int y2 = y[i] + dy[k]; if (ex[x2][y2] == -1) continue; if (ex[x2][y2] != -2 && ex[x2][y2] != k / 2) continue; // 葉は全部同一視できるので調べるのはどれか 1 つでいい. if (deg[x2][y2] == 1) { if (lx == -1) { lx = x2; ly = y2; lk = k; } } else { int ex_prv = ex[x2][y2]; if (ex[x2][y2] == -2) cost++; ex[x2][y2] = k / 2; rf(i + 1); if (ex_prv == -2) cost--; ex[x2][y2] = ex_prv; } } if (lx != -1) { int ex_prv = ex[lx][ly]; if (ex[lx][ly] == -2) cost++; ex[lx][ly] = lk / 2; rf(i + 1); if (ex_prv == -2) cost--; ex[lx][ly] = ex_prv; } }; rf(0); if (res == INF) res = -1; cout << res << endl; }