#ifndef LOCAL #define FAST_IO #endif // ============ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; // ============ #ifdef DEBUGF #else #define DBG(x) (void)0 #endif #line 2 "graph/mst/manhattan-mst.hpp" #line 2 "graph/graph-template.hpp" // https://ei1333.github.io/library/graph/mst/manhattan-mst.hpp /** * @brief Graph Template(グラフテンプレート) */ template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector< Edge< T > > &operator[](const int &k) { return g[k]; } inline const vector< Edge< T > > &operator[](const int &k) const { return g[k]; } }; template< typename T = int > using Edges = vector< Edge< T > >; #line 4 "graph/mst/manhattan-mst.hpp" /** * @brief Manhattan MST */ template< typename T > Edges< T > manhattan_mst(vector< T > xs, vector< T > ys) { assert(xs.size() == ys.size()); Edges< T > ret; int n = (int) xs.size(); vector< int > ord(n); iota(ord.begin(), ord.end(), 0); for(int s = 0; s < 2; s++) { for(int t = 0; t < 2; t++) { auto cmp = [&](int i, int j) -> bool { return xs[i] + ys[i] < xs[j] + ys[j]; }; sort(ord.begin(), ord.end(), cmp); map< T, int > idx; for(int i:ord) { for(auto it = idx.lower_bound(-ys[i]); it != idx.end(); it = idx.erase(it)) { int j = it->second; if(xs[i] - xs[j] < ys[i] - ys[j]) break; ret.emplace_back(i, j, abs(xs[i] - xs[j]) + abs(ys[i] - ys[j])); } idx[-ys[i]] = i; } swap(xs, ys); } for(int i = 0; i < n; i++) xs[i] *= -1; } return ret; } int main() { i32 n; cin >> n; Vec x(n), y(n); REP(i, n) { cin >> x[i] >> y[i]; } auto es = manhattan_mst(x, y); REP(i, n) { i32 a = x[i], b = y[i]; x[i] = a + b; y[i] = a - b; } i32 xmn = INF, xmx = -INF, ymn = INF, ymx = -INF; REP(i, n) { chmin(xmn, x[i]); chmax(xmx, x[i]); chmin(ymn, y[i]); chmax(ymx, y[i]); } Vec mx(n, 0); REP(i, n) { mx[i] = max({x[i] - xmn, xmx - x[i], y[i] - ymn, ymx - y[i]}); } Vec mn(n, INF); for (auto e : es) { chmin(mn[e.from], e.cost); chmin(mn[e.to], e.cost); } i32 ans = INF; REP(i, n) { chmin(ans, mx[i] - mn[i]); } cout << ans << '\n'; }