#ifndef HIDDEN_IN_VISUAL_STUDIO // 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 using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = 3.1415926535897932384626433832795; const double DEG = PI / 180.; // θ [deg] = θ * DEG [rad] const vi dx4 = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi dy4 = { 0, 1, 0, -1 }; const vi dx8 = { 1, 1, 0, -1, -1, -1, 0, 1 }; // 8 近傍 const vi dy8 = { 0, 1, 1, 1, 0, -1, -1, -1 }; const int INF = 1001001001; const ll INFL = 2002002002002002002LL; const double EPS = 1e-10; // 許容誤差に応じて調整 // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define distance (int)distance #define Yes(b) {cout << ((b) ? "Yes" : "No") << endl;} #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 < (1 << int(d)); ++set) // d ビット全探索(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 repit(it, a) for(auto it = (a).begin(); it != (a).end(); ++it) // イテレータを回す(昇順) #define repitr(it, a) for(auto it = (a).rbegin(); it != (a).rend(); ++it) // イテレータを回す(降順) #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 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template 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 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) // 演算子オーバーロード template inline istream& operator>> (istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline ostream& operator<< (ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template inline istream& operator>> (istream& is, tuple& t) { is >> get<0>(t) >> get<1>(t) >> get<2>(t); return is; } template inline ostream& operator<< (ostream& os, const tuple& t) { os << "(" << get<0>(t) << "," << get<1>(t) << "," << get<2>(t) << ")"; return os; } template inline istream& operator>> (istream& is, tuple& t) { is >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t); return is; } template inline ostream& operator<< (ostream& os, const tuple& t) { os << "(" << get<0>(t) << "," << get<1>(t) << "," << get<2>(t) << "," << get<3>(t) << ")"; return os; } template inline istream& operator>> (istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline ostream& operator<< (ostream& os, const vector& v) { repe(x, v) os << x << " "; return os; } template inline ostream& operator<< (ostream& os, const list& v) { repe(x, v) os << x << " "; return os; } template inline ostream& operator<< (ostream& os, const set& s) { repe(x, s) os << x << " "; return os; } template inline ostream& operator<< (ostream& os, const set>& s) { repe(x, s) os << x << " "; return os; } template inline ostream& operator<< (ostream& os, const unordered_set& s) { repe(x, s) os << x << " "; return os; } template inline ostream& operator<< (ostream& os, const map& m) { repe(p, m) os << p << " "; return os; } template inline ostream& operator<< (ostream& os, const unordered_map& m) { repe(p, m) os << p << " "; return os; } template inline ostream& operator<< (ostream& os, stack s) { while (!s.empty()) { os << s.top() << " "; s.pop(); } return os; } template inline ostream& operator<< (ostream& os, queue q) { while (!q.empty()) { os << q.front() << " "; q.pop(); } return os; } template inline ostream& operator<< (ostream& os, deque q) { while (!q.empty()) { os << q.front() << " "; q.pop_front(); } return os; } template inline ostream& operator<< (ostream& os, priority_queue q) { while (!q.empty()) { os << q.top() << " "; q.pop(); } return os; } template inline ostream& operator<< (ostream& os, priority_queue_rev q) { while (!q.empty()) { os << q.top() << " "; q.pop(); } return os; } template inline vector& operator--(vector& v) { rep(_i_, sz(v)) --v[_i_]; return v; } template inline vector& operator++(vector& v) { rep(_i_, sz(v)) ++v[_i_]; return v; } // 手元環境(Visual Studio) #ifdef _MSC_VER #define popcount (int)__popcnt // 全ビット中の 1 の個数 #define popcountll (int)__popcnt64 inline int lsb(unsigned int n) { unsigned long i; _BitScanForward(&i, n); return i; } // 最下位ビットの位置(0-indexed) inline int lsbll(unsigned long long n) { unsigned long i; _BitScanForward64(&i, n); return i; } inline int msb(unsigned int n) { unsigned long i; _BitScanReverse(&i, n); return i; } // 最上位ビットの位置(0-indexed) inline int msbll(unsigned long long n) { unsigned long i; _BitScanReverse64(&i, n); return i; } template T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } #define dump(x) cout << "\033[1;36m" << (x) << "\033[0m" << endl; #define dumps(x) cout << "\033[1;36m" << (x) << "\033[0m "; #define dumpel(a) { int _i_ = -1; cout << "\033[1;36m"; repe(x, a) {cout << ++_i_ << ": " << x << endl;} cout << "\033[0m"; } #define input_from_file(f) ifstream isTMP(f); cin.rdbuf(isTMP.rdbuf()); #define output_to_file(f) ofstream osTMP(f); cout.rdbuf(osTMP.rdbuf()); // 提出用(gcc) #else #define popcount (int)__builtin_popcount #define popcountll (int)__builtin_popcountll #define lsb __builtin_ctz #define lsbll __builtin_ctzll #define msb(n) (31 - __builtin_clz(n)) #define msbll(n) (63 - __builtin_clzll(n)) #define gcd __gcd #define dump(x) #define dumps(x) #define dumpel(v) #define input_from_file(f) #define output_to_file(f) #endif #endif // 折りたたみ用 //-----------------AtCoder 専用----------------- #include using namespace atcoder; //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); istream& operator>> (istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } ostream& operator<< (ostream& os, const mint& x) { os << x.val(); return os; } using vm = vector; using vvm = vector; using vvvm = vector; template ostream& operator<<(ostream& os, segtree seg) { int n = seg.max_right(0, [](S x) {return true; }); rep(i, n) os << seg.get(i) << " "; return os; } template ostream& operator<<(ostream& os, lazy_segtree seg) { int n = seg.max_right(0, [](S x) {return true; }); rep(i, n) os << seg.get(i) << " "; return os; } ostream& operator<<(ostream& os, dsu d) { repe(g, d.groups()) { repe(v, g) { os << v << " "; } os << endl; } return os; }; //---------------------------------------------- //【ビット列上 xor 作用付き 転倒数 モノイド】 /* * S ∋ x = {inv, c0, c1} : 列 x の転倒数,0 の個数,1 の個数の組 * F ∋ f : f との xor をとる作用を表す * x op y : 列 x, y を連結した列 * f mapping x : 列 x の各要素と f との xor をとった列 * f composition g : f xor g */ // verify : https://atcoder.jp/contests/practice12/tasks/practice12_l using S112 = tuple; using F112 = bool; S112 op112(S112 x, S112 y) { ll x_inv, y_inv, x_c0, x_c1, y_c0, y_c1; tie(x_inv, x_c0, x_c1) = x; tie(y_inv, y_c0, y_c1) = y; // まず x, y それぞれをソートするのに x_inv + y_inv 回の隣接互換が必要. // その後 x の右側に寄った x_c1 個の 1 と y の左側に寄った y_c0 個の 0 を // 交換するのに x_c1 * y_c0 回の隣接互換が必要. ll inv = x_inv + y_inv + x_c1 * y_c0; ll c0 = x_c0 + y_c0, c1 = x_c1 + y_c1; return { inv, c0, c1 }; } S112 e112() { return { 0LL, 0, 0 }; } S112 mapping112(F112 f, S112 x) { if (!f) return x; ll inv, c0, c1; tie(inv, c0, c1) = x; // 0 と 1 の組は全部で c0 * c1 個存在する. // そのうち inv 個が転倒していたのだから,転倒していないのは c0 * c1 - inv 個である. // ビット反転するとこれらが入れ替わるので,転倒数は c0 * c1 - inv になる. inv = c0 * c1 - inv; return { inv, c1, c0 }; } F112 composition112(F112 f, F112 g) { return f ^ g; } F112 id112() { return false; } #define XOR_inversion_mlop_monoid S112, op112, e112, F112, mapping112, composition112, id112 //【転倒数】O(n log n) /* * a[0..n) の転倒数を返す. */ template ll inversion_number(vector& a) { // verify : https://atcoder.jp/contests/arc075/tasks/arc075_c int n = sz(a); // 値 a[i] と添字 i を組にしソートする. vector> ai(n); rep(i, n) { ai[i] = { a[i], i }; } sort(all(ai)); ll res = 0; // ft[i] : いままでに添字 i の要素が現れたか fenwick_tree ft(n); // 値について昇順に見ていく. rep(j, n) { // id : 昇順で j 番目の値の添字 int id = ai[j].second; // id より大きい添字をもつ数が今までに何個あったかを加算する. res += ft.sum(id + 1, n); // 添字 id の出現を記録する. ft.add(id, 1); } return res; } void WA() { int m, k; cin >> m >> k; int n = m * k; vi a(n); cin >> a; vvi pos(m); rep(i, n) pos[a[i]].push_back(i); dumpel(pos); vector ini(n, { 0, 0, 1 }); lazy_segtree seg(ini); vl inv01(m + 1); rep(t, m) { inv01[t] = get<0>(seg.all_prod()); repe(i, pos[t]) { seg.set(i, { 0, 1, 0 }); } dump(seg); } dump(inv01); vi b(n), cnt(m); rep(i, n) { b[i] = a[i] + cnt[a[i]] * m; cnt[a[i]]++; } dump(b); ll inv = inversion_number(b); dump(inv); ll res = inv - *max_element(all(inv01)); cout << res << endl; } void naive() { int m, k; cin >> m >> k; int n = m * k; vi a(n); cin >> a; ll res = INFL; rep(hoge, m) { rep(i, n) a[i] = (a[i] + 1) % m; vi b(n), cnt(m); rep(i, n) { b[i] = a[i] + cnt[a[i]] * m; cnt[a[i]]++; } ll inv = inversion_number(b); chmin(res, inv); } cout << res << endl; } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); naive(); }