// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll using pii = pair; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #define oj_local(x, y) (y) #else #define dump(...) (void)(0) #define debug if (0) #define oj_local(x, y) (x) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream& os, tuple const& t) { bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; } template istream& operator>>(istream& is, tuple& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << '\n'; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template ()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); } template ()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); } template constexpr T min(set const& st) { assert(st.size()); return *st.begin(); } template constexpr T max(set const& st) { assert(st.size()); return *prev(st.end()); } template constexpr T min(multiset const& st) { assert(st.size()); return *st.begin(); } template constexpr T max(multiset const& st) { assert(st.size()); return *prev(st.end()); } constexpr ll max(signed x, ll y) { return max(x, y); } constexpr ll max(ll x, signed y) { return max(x, y); } constexpr ll min(signed x, ll y) { return min(x, y); } constexpr ll min(ll x, signed y) { return min(x, y); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; auto four_nbd(int n, int m) { static vector> v; return [n, m](int i, int j) { const int dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 }; v.clear(); rep (dir, 4) { int ni = i+dx[dir], nj = j+dy[dir]; if (0 <= ni and ni < n and 0 <= nj and nj < m) { v.emplace_back(ni, nj); } } return v; }; }; template vector iota(int n, Comp comp) { vector idx(n); iota(begin(idx), end(idx), 0); stable_sort(begin(idx), end(idx), comp); return idx; } constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template V &operator--(V &v) { for (auto &x : v) --x; return v; } template V &operator++(V &v) { for (auto &x : v) ++x; return v; } bool next_product(vector &v, int m) { repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0; return false; } bool next_product(vector &v, vector const& s) { repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0; return false; } template int sort_unique(vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template auto prefix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(s.back() + *l++); return s; } template auto suffix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(*--r + s.back()); reverse(s.begin(), s.end()); return s; } template T pop(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_back(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop(priority_queue &a) { auto x = a.top(); a.pop(); return x; } template T pop(queue &a) { auto x = a.front(); a.pop(); return x; } template T pop_front(deque &a) { auto x = a.front(); a.pop_front(); return x; } template T pop_back(deque &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_front(set &a) { auto x = *a.begin(); a.erase(a.begin()); return x; } template T pop_back(set &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template T pop_front(multiset &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; } template T pop_back(multiset &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } // <<< // >>> DST template struct DST : Handler { using Value = typename Handler::Value; using Handler::unit_value; // () -> Value using Handler::merge; // (Value, Value) -> Value static constexpr int bsr(int32_t x) { return x ? 31-__builtin_clz(x) : -1; } vector> v; DST() {} template DST(T&&... x) { build(forward(x)...); } void build(int n) { build(n, unit_value()); } void build(int n, Value const& x) { build(n, [&](int) { return x; }); } void build(vector const& v) { build(v.size(), [&](int i) { return v[i]; }); } template ()(0))> void build(int n, F gen) { assert(n >= 0); v.resize(1); v[0].resize(n, unit_value()); for (int i = 0; i < n; i++) v[0][i] = gen(i); if (n <= 1) return; const int lg = __lg(2*n-1); v.resize(lg, vector(n, unit_value())); for (int h = 1; h < lg; ++h) { const int w = 1<= b-w; --j) { v[h][j] = x = merge(v[0][j], x); } x = unit_value(); for (int j = b; j < min(n, b+w); ++j) { v[h][j] = x = merge(x, v[0][j]); } } } } int size() const { return v.empty() ? 0 : v[0].size(); } Value get(int l, int r) const { assert(0 <= l); assert(l <= r); assert(r <= size()); if (l == r) return unit_value(); --r; if (l == r) return v[0][l]; const int h = bsr(l^r); return merge(v[h][l], v[h][r]); } Value operator[](int idx) const { assert(0 <= idx); assert(idx < size()); return v[0][idx]; } }; // <<< // >>> segment tree template struct Segtree : Handler { using Value = typename Handler::Value; using Handler::unit_value; // () -> Value using Handler::merge; // (Value, Value) -> Value vector v; int n; Segtree() {} template Segtree(T&&... x) { init(forward(x)...); } template ()(0))> void init(int n, F gen) { assert(n >= 0); this->n = n; v.resize(2*n, unit_value()); for (int i = 0; i < n; i++) v[n+i] = gen(i); for (int i = n-1; i >= 1; i--) v[i] = merge(v[i<<1], v[i<<1|1]); } void init(int n) { init(n, [&](int) { return unit_value(); }); } void init(int n, Value const& x) { init(n, [&](int) { return x; }); } void init(vector const& v) { init(v.size(), [&](int i) { return v[i]; }); } int size() const { return n; } void set(int i, Value const& x) { assert(0 <= i); assert(i < size()); i += n; v[i] = x; while (i >>= 1) v[i] = merge(v[i<<1], v[i<<1|1]); } Value operator[](int i) const { return get(i); } Value get(int i) const { assert(0 <= i); assert(i < size()); return v[n + i]; } // [l, r) Value get(int l, int r) const { assert(0 <= l); assert(l <= r); assert(r <= size()); Value x = unit_value(), y = unit_value(); for (l += n, r += n; l < r; l >>= 1, r >>= 1) { if (l&1) x = merge(x, v[l++]); if (r&1) y = merge(v[--r], y); } return merge(x, y); } Value get_all() const { return get(0, size()); } template int max_right(int l, F f) { assert(0 <= l); assert(l <= size()); assert(f(unit_value())); l += n; const int r = size() << 1; Value x = unit_value(); while (true) { if (l == r) return size(); int k = __builtin_ctz(l | 1 << __lg(r - l)); auto y = merge(x, v[l >> k]); if (not f(y)) { l >>= k; break; } x = y, l += 1 << k; } while (l < size()) { auto y = merge(x, v[l <<= 1]); if (f(y)) x = y, l++; } return l - size(); } template int min_left(int r, F f) { assert(0 <= r); assert(r <= size()); assert(f(unit_value())); r += n; const int l = size(); Value x = unit_value(); while (true) { if (l == r) return 0; int k = __builtin_ctz(r | 1 << __lg(r - l)); auto y = merge(v[(r >> k) - 1], x); if (not f(y)) { r >>= k; --r; break; } x = y, r -= 1 << k; } while (r < size()) { r = r << 1 | 1; auto y = merge(v[r], x); if (f(y)) x = y, r--; } return r + 1 - size(); } vector dat() const { vector ret(size()); for (int i = 0; i < size(); i++) ret[i] = get(i); return ret; } }; // <<< struct Min { using Value = int; constexpr static Value unit_value() { return INF; } constexpr static Value merge(Value const& x, Value const& y) { return min(x, y); } }; struct Max { using Value = int; constexpr static Value unit_value() { return -INF; } constexpr static Value merge(Value const& x, Value const& y) { return max(x, y); } }; int32_t main() { int n; cin >> n; vector c(n+1), v(n+1); rep1 (i, n) cin >> c[i] >> v[i]; auto dp = make_v(n+1, n+1, -INF); dp[0][0] = 0; rep1R (k, n) { const int m = n/k; auto a = [&](int i, int w) { return dp[i][w] - i*v[k]; }; debug { auto DP = dp; DP.resize(n/(k+1)+1); dump(k, m, n/(k+1), as_mat(DP)); } repR (i, m+1) rep (w, n+1) if (not (i+1 < m+1 and w+k < n+1)) { static vector dat(n+1); static DST dst(n+1); dat.clear(); for (int pi = i, pw = w; pi >= 0 and pw >= 0; pi--, pw -= k) { dat.eb(a(pi, pw)); } dst.build(dat); for (int pi = i, pw = w; pi >= 0 and pw >= 0; pi--, pw -= k) { int l = i-pi, r = min(dst.size(), l+c[k]+1); chmax(dp[pi][pw], dst.get(l, r) + pi*v[k]); } } } rep1 (i, n) cout << max(dp[i]) << '\n'; }