#include #include #include #include #define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i)) #define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i)) #define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i)) #define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i)) #define ALL(x) std::begin(x), std::end(x) using namespace std; template inline void chmax(T & a, U const & b) { a = max(a, b); } template using rb_tree_set = __gnu_pbds::tree, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>; int64_t solve(int n, const vector & a) { // list queries for Mo's algorithm vector > queries; REP3 (k, 1, n + 1) { REP (i, n / k) { int l = k * i; int r = k * (i + 1); queries.emplace_back(l, r); } REP (i, n / k) { int l = n - k * (i + 1); int r = n - k * i; queries.emplace_back(l, r); } } // prepare the structure for Mo's algorithm rb_tree_set > used; int l = 0; int r = 0; auto add = [&](int i) { assert (i == l - 1 or i == r); used.insert(make_pair(a[i], i)); if (i == l - 1) -- l; if (i == r) ++ r; }; auto remove = [&](int i) { assert (i == l or i == r - 1); used.erase(make_pair(a[i], i)); if (i == l) ++ l; if (i == r - 1) -- r; }; auto get = [&]() { auto it = used.find_by_order((r - l - 1) / 2); assert (it != used.end()); return it->first; }; // run Mo's algorithm unordered_map median; sort(ALL(queries)); int sqrt_n = sqrt(n) + 3; for (int bl = 0, ql = 0; bl < n; ) { int br = min(n, bl + sqrt_n); int qr = ql; while (qr < queries.size() and queries[qr].first < br) { ++ qr; } sort(queries.begin() + ql, queries.begin() + qr, [&](pair a, pair b) { return a.second < b.second; }); REP3 (i, ql, qr) { int nl, nr; tie(nl, nr) = queries[i]; while (r < nr) add(r); while (nl < l) add(l - 1); while (nr < r) remove(r - 1); while (l < nl) remove(l); median[((uint64_t)nl << 32) | nr] = get(); } bl = br; ql = qr; } // compute the answer int64_t answer = INT64_MIN; vector left, right; REP3 (k, 1, n + 1) { int cnt = n / k; // list left groups int64_t sum_left = 0; left.assign(cnt + 1, 0); REP (i, cnt) { int l = k * i; int r = k * (i + 1); sum_left += median.at(((uint64_t)l << 32) | r); left[i + 1] = max(left[i], sum_left); } // list right groups int64_t sum_right = 0; right.assign(cnt + 1, 0); REP (i, cnt) { int l = n - k * (i + 1); int r = n - k * i; sum_right += median.at(((uint64_t)l << 32) | r); right[i + 1] = max(right[i], sum_right); } // convolution REP (i, left.size()) { int j = right.size() - i - 1; chmax(answer, k * (left[i] + right[j])); } } return answer; } int main() { int n; cin >> n; vector a(n); REP (i, n) { cin >> a[i]; } cout << solve(n, a) << endl; return 0; }