#include class Manager { size_t n; std::vector> C; struct node { size_t i, m; size_t limit; }; public: Manager(const std::vector> &D) : n(D.size()), C(D) { assert(C.size() + 1 == C[0].size()); } std::stack data; void add(const size_t i, const size_t m) { if (data.empty()) { data.push({i, m, n}); return; } else { while (data.top().limit < i + 1) { data.pop(); } const auto d = data.top(); if (C[d.i][i + 1] + d.m < C[i][i + 1] + m) { return; } } bool pushed = false; while (not data.empty()) { const auto d = data.top(); if (C[d.i][d.limit] + d.m > C[i][d.limit] + m) { data.pop(); } else { size_t ok = i + 1, ng = d.limit; while (ng - ok > 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({i, m, ok}); pushed = true; break; } } if (not pushed) { data.push({i, m, n}); } } size_t get_min(const size_t x) { while (data.top().limit < x) { data.pop(); } const auto d = data.top(); return C[d.i][x] + d.m; } void clear_log() { while (not data.empty()) { data.pop(); } } }; 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; } } Manager m(D); std::vector> dp(N + 1, std::vector(N + 1, N * N)); dp[0][0] = 0; for (size_t j = 0; j < N; ++j) { m.add(j, dp[j][j]); for (size_t i = j + 1; i <= N; ++i) { dp[i][j + 1] = m.get_min(i); if (i != N) { m.add(i, dp[i][j]); } } m.clear_log(); } for (size_t i = 1; i <= N; ++i) { std::cout << dp[N][i] << std::endl; } }