#include class CHTmodoki { size_t n; std::vector> C; struct node { size_t i, m; // f(x) = C[i][x] + m size_t limit; // このノードの関数 f(x) が最小となる最小の x は limit }; std::vector data; public: CHTmodoki(const std::vector> &vec) : n(vec.size()), C(vec) { assert(C.size() + 1 == C[0].size()); } void add(const size_t i, const size_t m) { assert(i < n); bool pushed = false; if (not data.empty()) { const auto d = data[data.size() - 1]; if (C[d.i][n] + d.m <= C[i][n] + m) { return; } } while (not data.empty()) { const auto d = data[data.size() - 1]; if (C[d.i][d.limit] + d.m >= C[i][d.limit] + m) { data.pop_back(); } else { size_t ok = n, ng = std::max(i, d.limit); while (ok - ng > 1) { const auto mid = (ok + ng) / 2; if (C[d.i][mid] + d.m <= C[i][mid] + m) { ok = mid; } else { ng = mid; } } data.push_back({i, m, ok}); pushed = true; break; } } if (not pushed) { data.push_back({i, m, i + 1}); } } size_t get_min(const size_t x) { const auto itr = --std::partition_point(data.begin(), data.end(), [&](const node &v) { return v.limit <= x; }); return C[itr->i][x] + (itr->m); } void clear_log() { data.clear(); } }; int main() { size_t N; std::cin >> N; std::vector P(N); for (auto &e : P) { std::cin >> e; } std::vector> D(N, std::vector(N + 1)); for (size_t i = 0; i < N - 1; ++i) { std::vector R(N + 1); for (size_t j = 0; j <= i; ++j) { ++R[P[j]]; } for (size_t j = 1; j <= N; ++j) { R[j] += R[j - 1]; } size_t sum = 0; for (size_t j = i + 1; j < N; ++j) { sum += R[N] - R[P[j]]; D[i + 1][j + 1] = sum; } } CHTmodoki manager(D); std::vector> dp(N + 1, std::vector(N + 1, N * N)); dp[0][0] = 0; for (size_t j = 0; j < N; ++j) { manager.add(j, dp[j][j]); for (size_t i = j + 1; i <= N; ++i) { dp[i][j + 1] = manager.get_min(i); if (i != N) { manager.add(i, dp[i][j]); } } manager.clear_log(); } for (size_t i = 1; i <= N; ++i) { std::cout << dp[N][i] << std::endl; } }