// Problem: No.3306 Life is Easy? // Contest: yukicoder // URL: https://yukicoder.me/problems/no/3306 // Memory Limit: 512 MB // Time Limit: 2000 ms // // Powered by CP Editor (https://cpeditor.org) #line 2 "/root/AtCoder/Halc-Library/Template/Template.hpp" #include using namespace std; #line 8 "/root/AtCoder/Halc-Library/Template/InOut.hpp" inline void scan() {} inline void scan(int32_t &a) { std::cin >> a; } inline void scan(uint32_t &a) { std::cin >> a; } inline void scan(int64_t &a) { std::cin >> a; } inline void scan(uint64_t &a) { std::cin >> a; } inline void scan(char &a) { std::cin >> a; } inline void scan(float &a) { std::cin >> a; } inline void scan(double &a) { std::cin >> a; } inline void scan(long double &a) { std::cin >> a; } inline void scan(std::vector &vec) { for (int32_t i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } } inline void scan(std::string &a) { std::cin >> a; } template inline void scan(std::vector &vec); template inline void scan(std::array &vec); template inline void scan(std::pair &p); template inline void scan(T (&vec)[size]); template inline void scan(std::vector &vec) { for (auto &i : vec) scan(i); } template inline void scan(std::deque &vec) { for (auto &i : vec) scan(i); } template inline void scan(std::array &vec) { for (auto &i : vec) scan(i); } template inline void scan(std::pair &p) { scan(p.first); scan(p.second); } template inline void scan(T (&vec)[size]) { for (auto &i : vec) scan(i); } template inline void scan(T &a) { std::cin >> a; } inline void in() {} template inline void in(Head &head, Tail &...tail) { scan(head); in(tail...); } inline void print() { std::cout << ' '; } inline void print(const bool &a) { std::cout << a; } inline void print(const int32_t &a) { std::cout << a; } inline void print(const uint32_t &a) { std::cout << a; } inline void print(const int64_t &a) { std::cout << a; } inline void print(const uint64_t &a) { std::cout << a; } inline void print(const char &a) { std::cout << a; } inline void print(const char a[]) { std::cout << a; } inline void print(const float &a) { std::cout << a; } inline void print(const double &a) { std::cout << a; } inline void print(const long double &a) { std::cout << a; } inline void print(const std::string &a) { for (auto &&i : a) print(i); } template inline void print(const std::vector &vec); template inline void print(const std::array &vec); template inline void print(const std::pair &p); template inline void print(const T (&vec)[size]); template inline void print(const std::vector &vec) { if (vec.empty()) return; print(vec[0]); for (auto i = vec.begin(); ++i != vec.end();) { std::cout << ' '; print(*i); } } template inline void print(const std::deque &vec) { if (vec.empty()) return; print(vec[0]); for (auto i = vec.begin(); ++i != vec.end();) { std::cout << ' '; print(*i); } } template inline void print(const std::array &vec) { print(vec[0]); for (auto i = vec.begin(); ++i != vec.end();) { std::cout << ' '; print(*i); } } template inline void print(const std::pair &p) { print(p.first); std::cout << ' '; print(p.second); } template inline void print(const T (&vec)[size]) { print(vec[0]); for (auto i = vec; ++i != end(vec);) { std::cout << ' '; print(*i); } } template inline void print(const T &a) { std::cout << a; } inline void out() { std::cout << '\n'; } template inline void out(const T &t) { print(t); std::cout << '\n'; } template inline void out(const Head &head, const Tail &...tail) { print(head); std::cout << ' '; out(tail...); } inline void Yes(bool i = true) { out(i ? "Yes" : "No"); } inline void No(bool i = true) { out(i ? "No" : "Yes"); } inline void Takahashi(bool i = true) { out(i ? "Takahashi" : "Aoki"); } inline void Aoki(bool i = true) { out(i ? "Aoki" : "Takahashi"); } inline void Alice(bool i = true) { out(i ? "Alice" : "Bob"); } inline void Bob(bool i = true) { out(i ? "Bob" : "Alice"); } inline void First(bool i = true) { out(i ? "First" : "Second"); } inline void Second(bool i = true) { out(i ? "Second" : "First"); } inline void Possible(bool i = true) { out(i ? "Possible" : "Impossible"); } inline void Impossible(bool i = true) { out(i ? "Impossible" : "Possible"); } inline void fls() { std::flush(std::cout); } struct IOsetup { IOsetup() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(16); } } iosetup; #line 9 "/root/AtCoder/Halc-Library/Template/Util.hpp" using ll = int64_t; using ld = long double; using ull = uint64_t; using uint = uint32_t; using pll = std::pair; using pii = std::pair; using vl = std::vector; using vvl = std::vector>; using pdd = std::pair; using tuplis = std::array; template using pq = std::priority_queue, std::greater>; constexpr ll LINF = (1LL << 62) - (1LL << 31); constexpr int32_t INF = INT_MAX >> 1; constexpr ll MINF = 1LL << 40; constexpr ld DINF = std::numeric_limits::infinity(); constexpr int32_t MODD = 1000000007; constexpr int32_t MOD = 998244353; constexpr ld EPS = 1e-9; constexpr ld PI = 3.1415926535897932; const ll four[] = {0, 1, 0, -1, 0}; const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0}; template bool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } else return false; } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } else return false; } template ll sum(const T &a) { return accumulate(std::begin(a), std::end(a), 0LL); } template ld dsum(const T &a) { return accumulate(std::begin(a), std::end(a), 0.0L); } template auto min(const T &a) { return *min_element(std::begin(a), std::end(a)); } template auto max(const T &a) { return *max_element(std::begin(a), std::end(a)); } #line 1 "/root/AtCoder/Halc-Library/Template/Macro.hpp" #define _overload3(_1, _2, _3, name, ...) name #define _overload4(_1, _2, _3, _4, name, ...) name #define _rep1(i, n) for (int64_t i = 0; i < (n); i++) #define _rep2(i, a, b) for (int64_t i = (a); i < (b); i++) #define _rep3(i, a, b, c) for (int64_t i = (a); i < (b); i += (c)) #define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__) #define _rrep1(i, n) for (int64_t i = (n) - 1; i >= 0; i--) #define _rrep2(i, a, b) for (int64_t i = (b) - 1; i >= (a); i--) #define rrep(...) _overload3(__VA_ARGS__, _rrep2, _rrep1)(__VA_ARGS__) #define each(i, ...) for (auto&& i : __VA_ARGS__) #define all(i) std::begin(i), std::end(i) #define rall(i) std::rbegin(i), std::rend(i) #define len(x) ((int64_t)(x).size()) #define fi first #define se second #define uniq(x) x.erase(unique(all(x)), std::end(x)) #define vec(type, name, ...) vector name(__VA_ARGS__); #define vv(type, name, h, ...) std::vector> name(h, std::vector(__VA_ARGS__)); #define INT(...) int32_t __VA_ARGS__; in(__VA_ARGS__) #define LL(...) int64_t __VA_ARGS__; in(__VA_ARGS__) #define ULL(...) uint64_t __VA_ARGS__; in(__VA_ARGS__) #define STR(...) std::string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define LD(...) long double __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) std::vector name(size); in(name) #define VV(type, name, h, w) std::vector> name(h, std::vector(w)); in(name) #line 2 "main.cpp" template struct NetworkSimplex { private: struct Edge { int to; Cap cap; Cost cost; int idx; }; template struct CSR { struct Range { std::vector::iterator bg, ed; std::vector::iterator begin() const { return bg; } std::vector::iterator end() const { return ed; } int size() const { return ed - bg; } E &operator[](int i) const { return bg[i]; } }; vector> given_e; vector e_elem; vector pos; int sz; CSR(int n) : sz(n), pos(n + 1, 0) {} void add(int p, E e) { given_e.emplace_back(p, e); pos[p + 1]++; } void build() { for (int i = 0; i < sz; i++) pos[i + 1] += pos[i]; e_elem.resize(pos.back()); for (int i = 0; i < pos.back(); i++) { e_elem[pos[given_e[i].first]] = given_e[i].second; pos[given_e[i].first]++; } for (int i = sz - 1; i >= 0; i--) { pos[i + 1] = pos[i]; } pos[0] = 0; } Range operator[](int u) { return Range{e_elem.begin() + pos[u], e_elem.begin() + pos[u + 1]}; } }; void add_linked(CSR> &list, int idx, int pos) { int last = list[idx][list[idx].size() - 1].first; list[idx][last].second = pos + 1; list[idx][list[idx].size() - 1].first = pos + 1; list[idx][pos + 1].first = last; list[idx][pos + 1].second = list[idx].size() - 1; } void erase_linked(CSR> &list, int idx, int pos) { int left = list[idx][pos + 1].first, right = list[idx][pos + 1].second; list[idx][left].second = right; list[idx][right].first = left; list[idx][pos + 1] = {-1, -1}; } public: int n; TotalCost total_cost = 0; vector lowers; vector b; CSR g; // vector> g; vector> edges; // b:supply-demand NetworkSimplex(int sz) : n(sz), g(sz), b(sz) {} // add supply/demand void add_excess(int v, Cap c) { b[v] += c; } // s->t l<=f<=u cost=c void add_edge(int s, int t, Cap l, Cap u, Cost c) { lowers.push_back(l); edges.emplace_back(-1, -1); total_cost += TotalCost(c) * TotalCost(l); b[s] -= l; b[t] += l; if (s != t) { edges.back() = {s, g.pos[s + 1]}; g.add(s, {t, u - l, c, g.pos[t + 1]}); g.add(t, {s, 0, -c, g.pos[s + 1] - 1}); } else if (c < 0) { total_cost += TotalCost(c) * TotalCost(u - l); lowers.back() += u - l; } } struct FlowResult { bool feasible; TotalCost cost; vector flow; vector potential; }; FlowResult solve() { int zs = g.pos[1]; for (int i = 1; i < n; i++) { g.add(0, {i, 0, 0, g.pos[i + 1]}); g.add(i, {0, 0, 0, g.pos[1] - 1}); } g.build(); vector level(n); vector iter(n); int mn; auto dfs = [&](auto self, int v, Cap f) -> Cap { if (b[v] < 0) { b[v] += f; return f; } if (level[v] >= mn) return 0; for (int &i = iter[v]; i < g[v].size(); i++) { Edge &e = g[v][i]; if (e.cap == 0 || level[v] >= level[e.to]) continue; Cap d = self(self, e.to, min(f, e.cap)); if (d > 0) { e.cap -= d; g[e.to][e.idx].cap += d; if (b[v] > 0) { b[v] -= d; if (b[v] == 0) return d; f = min(f, b[v]); } else { return d; } } } return 0; }; while (true) { fill(level.begin(), level.end(), -1); fill(iter.begin(), iter.end(), 0); queue q; for (int i = 0; i < n; i++) { if (b[i] > 0) { q.push(i); level[i] = 0; } } while (!q.empty()) { int v = q.front(); q.pop(); for (auto &e : g[v]) { if (e.cap > 0 && level[e.to] == -1) { level[e.to] = level[v] + 1; q.push(e.to); } } } mn = n; for (int i = 0; i < n; i++) { if (b[i] < 0 && level[i] != -1) mn = min(mn, level[i]); } if (mn == n) break; stack> pos; for (int i = 0; i < n; i++) { int cnt = 0; if (b[i] > 0) { dfs(dfs, i, b[i]); } } } for (int i = 0; i < n; i++) { if (b[i] != 0) return {false, 0, {}, {}}; } fill(level.begin(), level.end(), -1); for (int i = 0; i < n; i++) { if (level[i] != -1) continue; while (true) { fill(iter.begin(), iter.end(), -1); stack pos; iter[i] = 0; pos.push(i); vector> cycle; while (!pos.empty()) { int v = pos.top(); level[v] = 0; int used = -1; if (pos.size() > 1) { pos.pop(); used = g[pos.top()][iter[pos.top()]].idx; pos.push(v); } bool flg = false; for (int &j = iter[v]; j < g[v].size(); j++) { Edge &e = g[v][j]; if (e.cap == 0 || g[e.to][e.idx].cap == 0 || j == used) continue; if (iter[e.to] == -1) { iter[e.to] = 0; pos.push(e.to); flg = true; break; } if (iter[e.to] < g[e.to].size()) { while (true) { int nv = pos.top(); cycle.emplace_back(nv, iter[nv]); pos.pop(); if (nv == e.to) break; } break; } } if (!cycle.empty()) break; if (flg) continue; pos.pop(); if (pos.empty()) break; iter[pos.top()]++; } if (cycle.empty()) break; Cost sm = 0; Cap mn = numeric_limits::max(); for (auto &p : cycle) { Edge &e = g[p.first][p.second]; sm += e.cost; mn = min(mn, e.cap); } if (sm <= 0) { for (auto &p : cycle) { Edge &e = g[p.first][p.second]; e.cap -= mn; g[e.to][e.idx].cap += mn; } } else { mn = numeric_limits::max(); for (auto &p : cycle) { Edge &e = g[p.first][p.second]; mn = min(mn, g[e.to][e.idx].cap); } for (auto &p : cycle) { Edge &e = g[p.first][p.second]; e.cap += mn; g[e.to][e.idx].cap -= mn; } } } } CSR> tree(n); for (int i = 0; i < n; i++) { tree.add(i, {-1, g[i].size() + 1}); rep(_, g[i].size()) { tree.add(i, {-1, -1}); } tree.add(i, {0, -1}); } tree.build(); fill(level.begin(), level.end(), -1); vector p(n, 0); vector parent(n, -1); vector> can; for (int i = 0; i < n; i++) { if (level[i] != -1) continue; stack q; q.push(i); if (i == 0) level[i] = 0; else level[i] = 1; p[i] = 0; if (i != 0) { parent[i] = g[0][zs + i - 1].idx; add_linked(tree, 0, zs + i - 1); add_linked(tree, g[0][zs + i - 1].to, g[0][zs + i - 1].idx); } while (!q.empty()) { int v = q.top(); q.pop(); for (int i = 0; i < g[v].size(); i++) { Edge &e = g[v][i]; if (e.cap == 0 || g[e.to][e.idx].cap == 0 || level[e.to] != -1) { if (e.cap != 0) { if (g[e.to][e.idx].cap == 0) can.emplace_back(v, i); else parent[v] = i; } continue; } level[e.to] = level[v] + 1; p[e.to] = p[v] + e.cost; q.push(e.to); add_linked(tree, v, i); add_linked(tree, e.to, e.idx); } } } while (true) { pair mn = {numeric_limits::max(), -1}; for (int i = 0; i < can.size(); i++) { Edge &e = g[can[i].first][can[i].second]; if (e.cap == 0) continue; mn = min(mn, {e.cost + p[can[i].first] - p[e.to], i}); } if (mn.first >= 0) break; vector gl = {can[mn.second].first}; int st = g[can[mn.second].first][can[mn.second].second].to; vector> ncyc = {can[mn.second]}; while (st != gl.back()) { if (level[st] < level[gl.back()]) { gl.emplace_back(g[gl.back()][parent[gl.back()]].to); } else { ncyc.emplace_back(st, parent[st]); st = g[st][parent[st]].to; } } for (int i = gl.size() - 2; i >= 0; i--) { ncyc.emplace_back(gl[i + 1], g[gl[i]][parent[gl[i]]].idx); } Cap mc = numeric_limits::max(); for (auto &i : ncyc) mc = min(mc, g[i.first][i.second].cap); int del = -1; for (int i = 0; i < ncyc.size(); i++) { Edge &e = g[ncyc[i].first][ncyc[i].second]; e.cap -= mc; if (e.cap == 0) del = i; g[e.to][e.idx].cap += mc; } if (del == 0) { can[mn.second] = { g[can[mn.second].first][can[mn.second].second].to, g[can[mn.second].first][can[mn.second].second].idx}; continue; } erase_linked(tree, ncyc[del].first, ncyc[del].second); erase_linked(tree, g[ncyc[del].first][ncyc[del].second].to, g[ncyc[del].first][ncyc[del].second].idx); add_linked(tree, can[mn.second].first, can[mn.second].second); add_linked(tree, g[can[mn.second].first][can[mn.second].second].to, g[can[mn.second].first][can[mn.second].second].idx); can[mn.second] = {g[ncyc[del].first][ncyc[del].second].to, g[ncyc[del].first][ncyc[del].second].idx}; fill(level.begin(), level.end(), -1); level[0] = 0; stack q; q.push(0); while (!q.empty()) { int v = q.top(); q.pop(); int pos = 0; while (true) { int np = tree[v][pos].second; pos = np; np--; if (np >= g[v].size()) break; Edge &e = g[v][np]; if (level[e.to] != -1) { parent[v] = np; continue; } p[e.to] = p[v] + e.cost; level[e.to] = level[v] + 1; q.push(e.to); } } } for (int i = 0; i < edges.size(); i++) { int s = edges[i].first, t = edges[i].second; if (s == -1) continue; Edge &e = g[s][t]; lowers[i] += g[e.to][e.idx].cap; total_cost += TotalCost(e.cost) * TotalCost(g[e.to][e.idx].cap); } return {true, total_cost, lowers, p}; } }; void solve() { LL(N,M); VV(ll,A,N,M); ll day=N/2; NetworkSimplex gr(day*2); if(N==1){ ll ans=0; rep(i,day){ ans+=A[N-i-1][0]-A[i][0]; } out(ans); return; } if(N==2){ vl s1,s2; ll ans=0; rep(i,day){ ans+=A[N-i-1][0]-A[i][0]; s1.push_back(A[N-i-1][1]-A[N-i-1][0]); s2.push_back(A[i][0]-A[i][1]); } sort(all(s1)); sort(all(s2)); ll fin=ans; rrep(i,day){ ans+=s1[i]+s2[i]; chmax(fin,ans); } out(fin); return; } rep(i,day){ rep(j,day){ ll mx=0; rep(k,M){ chmax(mx,A[N-j-1][k]-A[i][k]); } gr.add_edge(i,j+day,0,1,-mx); } gr.add_excess(i,1); gr.add_excess(i+day,-1); } out(-gr.solve().cost); } int main() { solve(); }