#pragma region Macros #include using namespace std; template inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } #ifdef DEBUG template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '{'; for(int i = 0; i < (int)v.size(); i++) { if(i) { os << ','; } os << v[i]; } os << '}'; return os; } void debugg() { cerr << endl; } template void debugg(const T &x, const Args &... args) { cerr << " " << x; debugg(args...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif struct Setup { Setup() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __Setup; using ll = long long; #define OVERLOAD3(_1, _2, _3, name, ...) name #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define REP1(i, n) for(int i = 0; i < int(n); i++) #define REP2(i, a, b) for(int i = (a); i < int(b); i++) #define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__) #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define REVERSE(v) reverse(ALL(v)) #define SZ(v) ((int)(v).size()) const int INF = 1 << 30; const ll LLINF = 1LL << 60; constexpr int MOD = 1000000007; constexpr int MOD2 = 998244353; const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; void Case(int i) { cout << "Case #" << i << ": "; } int popcount(int x) { return __builtin_popcount(x); } ll popcount(ll x) { return __builtin_popcountll(x); } #pragma endregion Macros #line 2 "data-structure-2d/fenwick-tree-on-range-tree.hpp" // S ... size_type // T ... value_type template struct FenwickRangeTree { struct BIT { int N; vector data; BIT() = default; BIT(int size) { init(size); } void init(int size) { N = size; data.assign(N + 1, 0); } void add(int k, T x) { for (++k; k <= N; k += k & -k) data[k] += x; } T sum(int k) const { T ret = T(); for (; k; k -= k & -k) ret += data[k]; return ret; } inline T sum(int l, int r) const { T ret = T(); while (l != r) { if (l < r) { ret += data[r]; r -= r & -r; } else { ret -= data[l]; l -= l & -l; } } return ret; } }; using P = pair; S N, M; vector bit; vector> ys; vector

ps; FenwickRangeTree() = default; void add_point(S x, S y) { ps.push_back(make_pair(x, y)); } void build() { sort(begin(ps), end(ps)); ps.erase(unique(begin(ps), end(ps)), end(ps)); N = ps.size(); bit.resize(N + 1); ys.resize(N + 1); for (int i = 0; i <= N; ++i) { for (int j = i + 1; j <= N; j += j & -j) ys[j].push_back(ps[i].second); sort(begin(ys[i]), end(ys[i])); ys[i].erase(unique(begin(ys[i]), end(ys[i])), end(ys[i])); bit[i].init(ys[i].size()); } } int id(S x) const { return lower_bound( begin(ps), end(ps), make_pair(x, S()), [](const P& a, const P& b) { return a.first < b.first; }) - begin(ps); } int id(int i, S y) const { return lower_bound(begin(ys[i]), end(ys[i]), y) - begin(ys[i]); } void add(S x, S y, T a) { int i = lower_bound(begin(ps), end(ps), make_pair(x, y)) - begin(ps); assert(ps[i] == make_pair(x, y)); for (++i; i <= N; i += i & -i) bit[i].add(id(i, y), a); } T sum(S x, S y) const { T ret = T(); for (int a = id(x); a; a -= a & -a) ret += bit[a].sum(id(a, y)); return ret; } T sum(S xl, S yl, S xr, S yr) const { T ret = T(); int a = id(xl), b = id(xr); while (a != b) { if (a < b) { ret += bit[b].sum(id(b, yl), id(b, yr)); b -= b & -b; } else { ret -= bit[a].sum(id(a, yl), id(a, yr)); a -= a & -a; } } return ret; } }; /* * @brief 領域木(Binary Indexed Tree) */ void solve() { int N; cin >> N; vector x(N), y(N); REP(i, N) cin >> x[i] >> y[i]; vector mxs(N, -INF), mns(N, -INF); // max { vector ord(N); iota(ALL(ord), 0); sort(ALL(ord), [&](int i, int j) { return (x[i] + y[i] < x[j] + y[j]); }); REP(i, N) { int L = ord[0], R = ord[N-1]; int idx = ord[i]; chmax(mxs[idx], abs((x[idx] + y[idx]) - (x[L] + y[L]))); chmax(mxs[idx], abs((x[idx] + y[idx]) - (x[R] + y[R]))); } iota(ALL(ord), 0); sort(ALL(ord), [&](int i, int j) { return (x[i] - y[i] < x[j] - y[j]); }); REP(i, N) { int L = ord[0], R = ord[N-1]; int idx = ord[i]; chmax(mxs[idx], abs((x[idx] - y[idx]) - (x[L] - y[L]))); chmax(mxs[idx], abs((x[idx] - y[idx]) - (x[R] - y[R]))); } } debug(mxs); // min { FenwickRangeTree bt; REP(i, N) bt.add_point(x[i] + y[i], x[i] - y[i]); bt.build(); REP(i, N) bt.add(x[i] + y[i], x[i] - y[i], 1); REP(i, N) { int U = x[i] + y[i], V = x[i] - y[i]; auto check = [&](int d) -> bool { int s = bt.sum(U - d, V - d, U + d + 1, V + d + 1); return s > 1; }; int ok = 3*N + 5, ng = 0; while(ok - ng > 1) { int mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } mns[i] = ok; } } debug(mns); int ans = INF; REP(i, N) chmin(ans, mxs[i] - mns[i]); cout << ans << endl; } int main() { int T = 1; // cin >> T; while(T--) solve(); }