1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
#include "bits/stdc++.h"

using namespace std;

using LL = long long;
const int N = 1e6;
const int BUCKET_SIZE = 2000;
const int N_BUCKETS = 2000;

struct line {
  LL a;
  LL b;
  LL operator()(int x){
    return (LL) a * x + b;
  }
};

line raw_lines[N];

struct bucket {
  pair<LL, line*> envelope[BUCKET_SIZE];
  int envelope_size;
  int j;
  int j_position;

  line* lines;
  int bucket_size;
  
  LL addend;
  void increment_j();
  void rebuild_envelope();
  pair<LL, line*> score();

} buckets[N_BUCKETS];

void bucket::increment_j(){
  ++j;
  if(j_position + 1 < envelope_size && envelope[j_position + 1].first <= j) {
    ++j_position;
  }
}


LL div_ceil(LL x, LL y){
  if(y < 0){x = -x; y = -y;}
  if(x >= 0) return (x+y-1)/y;
  return -((-x)/y);
}

void bucket::rebuild_envelope(){
  envelope_size = 0;
  j_position = 0;
  for(int i = 0; i < bucket_size; ++i){
    line l1 = lines[i];
    if(l1.b == -1) continue;
    //cerr << "we can use line: " << i << "\n";
    while(envelope_size > 0 &&
      (*envelope[envelope_size - 1].second)(envelope[envelope_size - 1].first)
          <= l1(envelope[envelope_size - 1].first)) {
      envelope_size--;
    }
    if(envelope_size == 0 || envelope[envelope_size - 1].second->a == l1.a){
      envelope[envelope_size++] = {j, lines + i};
      continue;
    }
    line l0 = *envelope[envelope_size - 1].second;
    LL x = div_ceil(l0.b-l1.b, l1.a-l0.a);
    if(x > N) continue;
    envelope[envelope_size++] = {x, lines + i};
  }
}

pair<LL, line*> bucket::score(){
  if(envelope_size == 0) return {-2, lines + bucket_size};
  return {(*envelope[j_position].second)(j) + addend, envelope[j_position].second};
}

void test_bucket(){
  {
    bucket b;
    line lines[3];
    lines[0] = {0, 3};
    lines[1] = {1, 0};
    lines[2] = {2, 0};
    b.lines = lines;
    b.bucket_size = 3;
    b.j = 0;
    b.rebuild_envelope();
    assert(b.envelope_size == 2);
    assert(b.envelope[0] == make_pair(0LL, lines + 0));
    assert(b.envelope[1] == make_pair(2LL, lines + 2));
    assert(b.j == 0);
    assert(b.j_position == 0);
    b.increment_j();
    assert(b.j == 1);
    assert(b.j_position == 0);
    b.increment_j();
    assert(b.j == 2);
    assert(b.j_position == 1);
  }
  {
    bucket b;
    line lines[3];
    lines[0] = {0, 5};
    lines[1] = {2, 2};
    lines[2] = {3, 0};
    b.lines = lines;
    b.bucket_size = 3;
    b.j = 0;
    b.rebuild_envelope();
    assert(b.envelope_size == 2);
    assert(b.envelope[0] == make_pair(0LL, lines + 0));
    assert(b.envelope[1] == make_pair(2LL, lines + 2));
    assert(b.j == 0);
    assert(b.j_position == 0);
    b.increment_j();
    assert(b.j == 1);
    assert(b.j_position == 0);
    b.increment_j();
    assert(b.j == 2);
    assert(b.j_position == 1);
    b.increment_j();
    assert(b.j == 3);
    assert(b.j_position == 1);
  }
}

int main(){
  // test_bucket();
  int n;
  cin >> n;
  for(int i = 0; i < n; ++i){
    cin >> raw_lines[i].a >> raw_lines[i].b;
  }

  sort(raw_lines, raw_lines + n, [](const line &l0, const line &l1){
    if(l0.a == l1.a) return l0.b < l1.b;
    return l0.a < l1.a;
  });

  //for(int i = 0; i < n; i++) cerr << raw_lines[i].a << " " << raw_lines[i].b << "\n";

  int n_buckets = min(N_BUCKETS, max(1, (int) (sqrt(n) * 0.70)));
  for(int bucket_i = 0; bucket_i < n_buckets; ++bucket_i) {
    buckets[bucket_i].j = 0;
    int i0 = (LL) bucket_i * n / n_buckets;
    int i1 = (LL) (bucket_i + 1) * n / n_buckets;
    //cerr << "i0 = " << i0 << "\n";
    //cerr << "i1 = " << i1 << "\n";
    buckets[bucket_i].lines = raw_lines + i0;
    buckets[bucket_i].bucket_size = i1 - i0;
    buckets[bucket_i].addend = 0;
    buckets[bucket_i].rebuild_envelope();
  }
  LL total = 0;
  for(int i = 0; i < n; i++){
    //for(int i = 0; i < n; i++) cout << raw_lines[i].b << " "; cout << "\n";
    pair<pair<LL, line*>, int> best({-1, nullptr}, n_buckets);
    for(int bucket_i = 0; bucket_i < n_buckets; ++bucket_i) {
      //cerr << "bucket_i = " << bucket_i << "\n";
      //for(int j = 0; j < buckets[bucket_i].envelope_size; ++j){
        //cerr << "x = " << buckets[bucket_i].envelope[j].first;
        //cerr << " line = " << buckets[bucket_i].envelope[j].second - raw_lines << "\n";
      //}
      auto cand = buckets[bucket_i].score();
      //cerr << "cand score = " << cand.first << "\n";
      //cerr << "cand line = " << cand.second - raw_lines << "\n";

      best = max(best, make_pair(cand, bucket_i));
    }

    //cerr << "best score = " << best.first.first << "\n";
    //cerr << "best line = " << best.first.second - raw_lines << "\n";

    int best_bucket = best.second;
    
    for(int bucket_j = 0; bucket_j < best_bucket; ++bucket_j){
      buckets[bucket_j].addend += best.first.second->a;
    }
    
    for(line *l = buckets[best_bucket].lines; l != best.first.second; ++l) {
      if(l->b != -1){
        l->b += best.first.second->a;
      }
    }
    best.first.second->b = -1;
    for(line *l = best.first.second + 1;
        l != buckets[best_bucket].lines + buckets[best_bucket].bucket_size;
        ++l) {
      if(l->b != -1){
        l->b += l->a;
      }
    }
    buckets[best_bucket].rebuild_envelope();

    for(int bucket_j = best_bucket + 1; bucket_j < n_buckets; ++bucket_j){
      buckets[bucket_j].increment_j();
    }

    total += best.first.first;
    cout << total << "\n";
  }
}