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
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
#include <bits/stdc++.h>
#define all(x) (x).begin(),(x).end()
using namespace std;

using ll = long long;
//using ld = long double;

//#define int ll
#define sz(x) ((int)(x).size())

using pii = pair<int,int>;
using tii = tuple<int,int,int>;
using tiii = tuple<int,int,int,int>;


const int mod = 1e9 + 7, nmax = 1e6 + 5;
struct Mint {
  int val;
  Mint(ll x = 0): val((x % mod + mod) % mod) {;}
  Mint operator +(const Mint& x) { return Mint(val + x.val); }
  Mint operator -(const Mint& x) { return Mint(val - x.val); }
  Mint operator *(const Mint& x) { return Mint((ll)val * x.val); }
  Mint operator +=(const Mint& x) { return *this = Mint(val + x.val); }
  Mint operator -=(const Mint& x) { return *this = Mint(val - x.val); }
  Mint operator *=(const Mint& x) { return *this = Mint((ll)val * x.val); }
  Mint operator ^(const int& _b) const {
    Mint accum = 1, a = *this;
    int b = _b;
    while(b) {
      accum = (b & 1? accum * a : accum);
      a *= a;
      b >>= 1;
    }
    return accum;
  }
  Mint operator /(const Mint& x) { return Mint((ll)val * (x ^ (mod - 2)).val); }
  Mint operator /=(const Mint& x) { return *this = Mint((ll)val * (x ^ (mod - 2)).val); }
};

vector<vector<pii>> divisions;

namespace Recolor {
   set<int> starts;
   int atr_ends[nmax];
   int atr_color[nmax];
   
   int CC[nmax];
   
   int query(int p) {
      //return CC[p];
      return atr_color[*prev(starts.upper_bound(p))];
   }
   
   vector<int> color(int l, int r, int C) {
      
      if(prev(starts.upper_bound(l)) == prev(starts.upper_bound(r + 1))) {
         auto it = prev(starts.upper_bound(l));
         auto elements = vector<int>{atr_color[*it]};
         atr_ends[r + 1] = atr_ends[*it];
         atr_ends[*it] = l - 1;
         atr_color[r + 1] = atr_color[*it];
         
         atr_color[l] = C;
         atr_ends[l] = r;
         starts.emplace(l);
         starts.emplace(r + 1);

         return elements;
      }
      
      
      vector<int> elements;
      
      auto it = prev(starts.upper_bound(l));
      elements.emplace_back(atr_color[*it]);
      if(*it <= l - 1) {
         atr_ends[*it] = l - 1;
      }
      else
         starts.erase(it);
      
      while((it = starts.upper_bound(l)) != starts.end() && *it <= r) {
         //if(C == 81) cerr << " ! " << *it << ' ' << atr_ends[*it] << ' ' << atr_color[l] << '\n';
         elements.emplace_back(atr_color[*it]);
         if(atr_ends[*it] <= r) {
            starts.erase(it);
         }
         else {
            starts.emplace(r + 1);
            atr_color[r + 1] = atr_color[*it];
            atr_ends[r + 1] = atr_ends[*it];
            starts.erase(it);
         }
      }
      
      sort(all(elements));
      elements.erase(unique(all(elements)), end(elements));
      
      atr_ends[l] = r;
      atr_color[l] = C;
      starts.emplace(l);
      
      return elements;
   }
   
   void init(int n) {
      starts.emplace(0);
      atr_ends[0] = 2 * n + 1;
      atr_color[0] = 0;
      starts.emplace(2 * n + 2);
      return;
   }
}

namespace RectSum {
   vector<int> rez;
   vector<tiii> qs;
   
   void init() { rez.assign(1, 0); }
   
   int add_query(int h1, int h2, int l, int r) {
      int id = sz(rez);
      qs.emplace_back(h1, l, r, -id);
      qs.emplace_back(h2, l, r, id);
      rez.emplace_back(0);

      return id;
   }
   
   #define lsb(x) (x & -x)
   struct AIB {
      vector<int> tree;
      void init(int n) {
         tree.assign(n + 10, 0);
      }
      int query(int p) {
         int sum = 0;
         while(p > 0) sum += tree[p], p -= lsb(p);
         return sum;
      }
      void upd(int p, int x) {
         while(p < sz(tree)) tree[p] += x, p += lsb(p);
         return;
      }
      int query(int l, int r) { return query(r) - query(l - 1); }
   };
   
   void initialise_sums(vector<pii> pcts) {
      sort(all(pcts));
      sort(all(qs));
      int ptr = 0;
      
      AIB aib;
      aib.init(sz(pcts) * 2);
      
      for(auto [h, p] : pcts) {
         while(ptr < sz(qs) && get<0>(qs[ptr]) < h) {
            rez[abs(get<3>(qs[ptr]))] += ((abs(get<3>(qs[ptr]))) / (get<3>(qs[ptr]))) * aib.query(get<1>(qs[ptr]), get<2>(qs[ptr])),
            ptr++;
         }
         
         aib.upd(p, 1);
      }
      
      while(ptr < sz(qs)) {
         rez[abs(get<3>(qs[ptr]))] += ((abs(get<3>(qs[ptr]))) / (get<3>(qs[ptr]))) * aib.query(get<1>(qs[ptr]), get<2>(qs[ptr])),
         ptr++;
      }
      return;
   }
   
   int query(int id) { return rez[abs(id)] * (id / abs(id)); }
   
}

int highest_link[nmax], right_sum[nmax], left_sum[nmax];

int rd[nmax], rjump[nmax], rp[nmax];
int ld[nmax], ljump[nmax], lp[nmax];

int dom_d[nmax], dom_jump[nmax], dom_p[nmax];

struct dirLink {
   int level, crease, last;
} left_link[nmax], right_link[nmax];

vector<int> mergepoint_id[nmax];

int dom_lca(int a, int b) {
   if(dom_d[a] < dom_d[b]) swap(a, b);
   while(dom_d[a] > dom_d[b]) {
      if(dom_d[dom_jump[a]] > dom_d[b]) a = dom_jump[a];
      a = dom_p[a];
   }
   
   while(a != b) {
      if(dom_jump[a] != dom_jump[b])
         a = dom_jump[a],
         b = dom_jump[b];
      
      a = dom_p[a],
      b = dom_p[b];
   }
   //cerr << a << '\n';
   return a;
}

signed main() {
   cin.tie(0) -> sync_with_stdio(0);
   int n;
   cin >> n;
   RectSum::init();
   
   vector<pii> segm(n + 1);
   for(auto &[l, r] : segm | views::drop(1)) cin >> l >> r;
   segm[0] = pii{0, 2 * n + 1};
   reverse(1 + all(segm));
   
   { // highest link and creases initialisation
      Recolor::init(2 * n);
      int ptr = 1; // probabil ca ar fi mers mai bine daca spargeam artificial fiecare segment in left/right pointer (????), defapt nu, sa imi bag pula daca mai stiu ceva
      // stiu ca imi iau o mare muie, that is for sure
      for(auto [l, r] : segm | views::drop(1)) {         
         
         int LC = Recolor::query(l), RC = Recolor::query(r);
         
         
         int idom = LC;
         //for(int i = l; i <= r; i++)
            //idom = dom_lca(idom, Recolor::query(i));
         auto C = Recolor::color(l, r, ptr);
         for(auto i : C)
            idom = dom_lca(idom, i);
         
         highest_link[ptr] = idom;
         
         dom_d[ptr] = dom_d[idom] + 1;
         dom_jump[ptr] = dom_p[ptr] = idom;
         if(dom_d[idom] + dom_d[dom_jump[dom_jump[idom]]] == 2 * dom_d[dom_jump[idom]]) dom_jump[ptr] = dom_jump[dom_jump[idom]];
         
         lp[ptr] = ljump[ptr] = LC;
         rp[ptr] = rjump[ptr] = RC;
         
         ld[ptr] = ld[LC] + 1;
         rd[ptr] = rd[RC] + 1;
         
         if(ld[LC] + ld[ljump[ljump[LC]]] == 2 * ld[ljump[LC]]) ljump[ptr] = ljump[ljump[LC]];
         if(rd[RC] + rd[rjump[rjump[RC]]] == 2 * rd[rjump[RC]]) rjump[ptr] = rjump[rjump[RC]];
         
         int node_l = ptr, node_r = ptr;
         pii before_disaster(ptr, ptr);
         
         {
            while(ld[node_l] > ld[highest_link[ptr]]) {
               if(ld[ljump[node_l]] > ld[highest_link[ptr]]) node_l = ljump[node_l];
               before_disaster.first = node_l;
               node_l = lp[node_l];
            }
            
            
            while(rd[node_r] > rd[highest_link[ptr]]) {
               if(rd[rjump[node_r]] > rd[highest_link[ptr]]) node_r = rjump[node_r];
               before_disaster.second = node_r;
               node_r = rp[node_r];
            }
         }
         
         highest_link[ptr] = node_l;
         
            
         left_link[ptr].level = LC;
         right_link[ptr].level = RC;
         
         left_link[ptr].crease = RectSum::add_query(0, LC, segm[LC].first, l - 1);
         right_link[ptr].crease = RectSum::add_query(0, RC, r + 1, segm[RC].second);
      
      
         left_link[ptr].last = before_disaster.first;
         right_link[ptr].last = before_disaster.second;
      
         mergepoint_id[ptr].emplace_back(RectSum::add_query(0, ptr, l, r));
         mergepoint_id[ptr].emplace_back(RectSum::add_query(0, highest_link[ptr], segm[before_disaster.first].first, segm[before_disaster.second].second));
            
         ptr++;
      }
   }
   
   { // facem id-urile
      vector<pii> pcts;
      for(int i = 1; i <= n; i++)
         pcts.emplace_back(i, (segm[i].first + segm[i].second) / 2);
      
      RectSum::initialise_sums(pcts);
   } 
   
   { // acum calculam sumele
      Mint sum = 0;
      for(int i = 1; i <= n; i++) {
         right_sum[i] = right_sum[right_link[i].level] + RectSum::query(right_link[i].crease);
         left_sum[i] = left_sum[left_link[i].level] + RectSum::query(left_link[i].crease);
         
         int here = right_sum[i] + left_sum[i] - left_sum[left_link[i].last] - right_sum[right_link[i].last] + RectSum::query(mergepoint_id[i][0]) + RectSum::query(-mergepoint_id[i][1]);
         sum += Mint(1) / Mint(here);
      }
      cout << sum.val << '\n';
   }
   
}

/**
  Anul asta nu se da centroid
  -- Rugaciunile mele
*/