/** * date : 2024-08-02 01:46:13 * author : Nyaan */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template using minpq = priority_queue, greater>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(T &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template vector> product(const vector &a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I, const function &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function{[](T &) -> void {}}); } template T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector &v) { using U = typename T::value_type; if(v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template vector Rotate(const vector &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return __builtin_popcountll(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // using namespace std; // Line : T operator(ll) を定義する template struct LiChaoTree { using T = decltype(Line{}(0)); vector xs; vector dat; vector> val; // (評価点(座圧後), 評価した値) int n, size; T inf; LiChaoTree(const vector& _xs, Line I) { init(_xs, I); } LiChaoTree(int _n, Line I) { vector _xs(_n); for (int i = 0; i < _n; i++) _xs[i] = i; init(_xs, I); } int get_idx(long long x) { return lower_bound(begin(xs), end(xs), x) - begin(xs); } void add_line(Line f) { return apply(1, f); } // [xl, xr) 半開 void add_segment(long long xl, long long xr, Line f) { xl = get_idx(xl), xr = get_idx(xr); if (xl == xr) return; xl += size, xr += size; int l = xl, r = xr; for (; xl < xr; xl >>= 1, xr >>= 1) { if (xl & 1) apply(xl++, f); if (xr & 1) apply(--xr, f); } if (RANGE_GET) { for (int i = 1; i <= __builtin_ctz(size); i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } } // (値, Line) の組 pair get_val(long long x) { int i = get_idx(x); assert(0 <= i and i < n); Line f = dat[0]; T fx = f(x); for (i += size; i; i >>= 1) { Line g = dat[i]; T gx = g(x); if ((MINIMIZE && gx < fx) || (!MINIMIZE && gx > fx)) { f = g, fx = gx; } } return {fx, f}; } // [xl, xr) 半開 // 返り値 : (評価点 x, x で評価した値) // 追加する直線に単調性がある時のみ使用可能 // RANGE_GET を true にする必要がある pair get(long long xl, long long xr) { assert(RANGE_GET == true); xl = get_idx(xl), xr = get_idx(xr); assert(xl != xr); pair best = _get(1, 0, size, xl, xr); assert(best.first != -1); return make_pair(xs[best.first], best.second); } private: void init(const vector& _xs, Line I) { xs = _xs; sort(begin(xs), end(xs)); xs.erase(unique(begin(xs), end(xs)), end(xs)); n = xs.size(); int lg = 1; while ((1 << lg) < n) lg++; size = 1 << lg; dat.resize(size * 2, I); inf = (MINIMIZE ? numeric_limits::max() : numeric_limits::min()) / 2; val.resize(size * 2, make_pair(-1, inf)); for (int i = size * 2 - 1; i; i--) update(i); } T eval(int i, Line f) { return f(xs[min(i, n - 1)]); } void apply(int i, Line f) { int upper_bit = 31 - __builtin_clz(i); int l = (size >> upper_bit) * (i - (1 << upper_bit)); int r = l + (size >> upper_bit); Line g = dat[i]; T fl = eval(l, f), fr = eval(r - 1, f); T gl = eval(l, g), gr = eval(r - 1, g); bool bl = (MINIMIZE ? fl < gl : fl > gl); bool br = (MINIMIZE ? fr < gr : fr > gr); if (!bl and !br) return; if (bl and br) { dat[i] = f; } else { int m = (l + r) / 2; T fm = eval(m, f), gm = eval(m, g); bool bm = (MINIMIZE ? fm < gm : fm > gm); if (bm) { dat[i] = f; f = g; apply(i * 2 + bl, f); } else { apply(i * 2 + 1 - bl, f); } } update(i); } void update(int i) { if constexpr (RANGE_GET) { if (i == 0) return; int upper_bit = 31 - __builtin_clz(i); int l = (size >> upper_bit) * (i - (1 << upper_bit)); int r = l + (size >> upper_bit); val[i] = make_pair(-1, inf); auto chmin = [&](int x, T y) { if (MINIMIZE ? y < val[i].second : val[i].second < y) { val[i] = make_pair(x, y); } }; if (l < n) { chmin(l, eval(l, dat[i])); chmin(min(r - 1, n - 1), eval(r - 1, dat[i])); } if (i < size) { chmin(val[i * 2 + 0].first, val[i * 2 + 0].second); chmin(val[i * 2 + 1].first, val[i * 2 + 1].second); } } } pair _get(int idx, int l, int r, int xl, int xr) { assert(l < r and xl < xr); assert(l <= xl and xr <= r); if (xl == l and xr == r) return val[idx]; pair best = make_pair(-1, inf); auto chmin = [&](int x, T y) { if (MINIMIZE ? y < best.second : y > best.second) { best = make_pair(x, y); } }; chmin(xl, eval(xl, dat[idx])); chmin(xr - 1, eval(xr - 1, dat[idx])); int m = (l + r) / 2; if (xl < m) { auto [x, y] = _get(idx * 2 + 0, l, m, xl, min(xr, m)); chmin(x, y); } if (m < xr) { auto [x, y] = _get(idx * 2 + 1, m, r, max(xl, m), xr); chmin(x, y); } return best; } }; using namespace Nyaan; constexpr int nmax = 3030; ll cost[nmax][nmax]; ll dp[nmax], newdp[nmax]; struct F { int i; ll operator()(int j) { if (i == -1) return inf; return dp[i] - cost[i][j]; } }; void q() { ini(N); vi a(N); in(a); repr(L, N) reg(R, L, N + 1) { if (R - L <= 1) continue; cost[L][R] = cost[L + 1][R] + cost[L][R - 1] - cost[L + 1][R - 1] + (a[L] > a[R - 1]); trc(L, R, cost[L][R]); } fill(begin(dp), end(dp), inf); dp[0] = 0; rep1(n, N) { LiChaoTree lct(N + 1, F{-1}); rep(i, N + 1) { newdp[i] = lct.get_val(i).fi; lct.add_line(F{int(i)}); } swap(dp, newdp); trc(vi{dp, dp + N + 1}, cost[0][N]); out(cost[0][N] + dp[N]); } } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }