#include <bits/stdc++.h> #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using namespace std; __always_inline int rint() { static int res; static char c; res = 0; do { c = getchar_unlocked(); } while(!isdigit(c)); while(isdigit(c)) { res = 10 * res + c - '0', c = getchar_unlocked(); } return res; } __always_inline void pint(int x) { static int ptr; static char buff[20]; ptr = 0; do { buff[ptr++] = '0' + x % 10, x /= 10; } while(x); while(ptr) { putchar_unlocked(buff[--ptr]); } } #pragma GCC maksuje_zadania_na_essie("pot200"); #define loop(i, a, b) for(int i = a; i <= b; i++) #define loop_rev(i, a, b) for(int i = a; i >= b; i--) #define all(x) x.begin(), x.end() #define sz(x) int(x.size()) #define pb push_back using ll = int64_t; using ull = uint64_t; using uint = uint32_t; struct Shelf { int x1, x2, y; }; constexpr ll MOD = 1e9 + 7; ll mul(ll a, ll b) { return (a * b % MOD); } ll add(ll a, ll b) { return (a + b >= MOD ? a + b - MOD : a + b); } ll sub(ll a, ll b) { return (a - b < 0 ? a - b + MOD : a - b); } ll qpow(ll a, ll b) { ll res = 1; while(b) { if(b&1) res = mul(res, a); a = mul(a, a); b /= 2; } return res; } constexpr int MAX_N = 5e5 + 1; ll fact_inv[MAX_N]; ll fact[MAX_N]; constexpr int LOG = 19; int jmp[MAX_N][2][LOG]; int depth[MAX_N][2]; Shelf shelves[MAX_N]; int lg; int lift(int x, int h, int type) { int i = 0; while(h > 0) { if(x == (-1)) return (-1); if(h&1) { x = jmp[x][type][i]; } h /= 2; ++i; } return x; } int first_greater_end(int v, int x) { if(shelves[v].x2 > x) return v; loop_rev(i, lg-1, 0) { int new_v = jmp[v][1][i]; if(new_v != (-1) && shelves[new_v].x2 <= x) { v = new_v; } } return jmp[v][1][0]; } int first_smaller_start(int v, int x) { if(shelves[v].x1 < x) return v; loop_rev(i, lg-1, 0) { int new_v = jmp[v][0][i]; if(new_v != (-1) && shelves[new_v].x1 >= x) { v = new_v; } } return jmp[v][0][0]; } int lift_to(int v, int type, int dest) { int lifted = lift(v, depth[v][type] - depth[dest][type], type); if(lifted == dest) return dest; else return (-1); } int lca(int a, int b) { if(a == b) return a; if(b > a) { int l = 0, r = depth[b][0]; while(l < r) { int mid = (l+r)/2; int b_lifted = lift(b, mid, 0); int a_lifted = first_greater_end(a, shelves[b_lifted].x1); if(a_lifted == (-1) || shelves[a_lifted].y < shelves[b_lifted].y) { l = mid + 1; } else { r = mid; } } int final_b_lifted = lift(b, l, 0); int final_a_lifted = lift_to(a, 1, final_b_lifted); if(final_b_lifted == final_a_lifted) return final_a_lifted; } else { int l = 0, r = depth[a][1]; while(l < r) { int mid = (l+r)/2; int a_lifted = lift(a, mid, 1); int b_lifted = first_smaller_start(b, shelves[a_lifted].x2); if(b_lifted == (-1) || shelves[b_lifted].y < shelves[a_lifted].y) { l = mid + 1; } else { r = mid; } } int final_a_lifted = lift(a, l, 1); int final_b_lifted = lift_to(b, 0, final_a_lifted); if(final_a_lifted == final_b_lifted) return final_a_lifted; } return (-1); } int main() { cin.tie(0)->sync_with_stdio(false); int n = rint(); lg = int(log2(n)) + 1; vector<vector<vector<int>>> graph(n, vector<vector<int>>(2)); loop(i, 0, n-1) { loop(j, 0, LOG-1) { jmp[i][0][j] = jmp[i][1][j] = (-1); } } fact[0] = 1; loop(i, 1, n) fact[i] = mul(fact[i-1], i); fact_inv[n] = qpow(fact[n], MOD-2); loop_rev(i, n, 1) fact_inv[i-1] = mul(i, fact_inv[i]); loop(i, 0, n-1) { shelves[i].x1 = rint(); shelves[i].x2 = rint(); shelves[i].y = i; } set<tuple<int,int,int>> open; loop_rev(i, n-1, 0) { if(!open.empty()) { auto it = open.upper_bound({ shelves[i].x1, -1, -1 }); while(it != open.end() && get<0>(*it) < shelves[i].x2) { graph[get<1>(*it)][get<2>(*it)].pb(i); it = open.erase(it); } } open.emplace(shelves[i].x1, i, 0); open.emplace(shelves[i].x2, i, 1); } loop(i, 0, n-1) { loop(type, 0, 1) { jmp[i][type][0] = (-1); for(int s : graph[i][type]) { // cause it can be empty (jajo edge case) jmp[i][type][0] = s; loop(len, 1, lg-1) { if(jmp[i][type][len-1] != (-1)) { jmp[i][type][len] = jmp[jmp[i][type][len-1]][type][len-1]; } } } } } loop(i, 0, n-1) { loop(type, 0, 1) { if(graph[i][type].empty()) depth[i][type] = 0; else depth[i][type] = depth[graph[i][type][0]][type] + 1; } } vector<int> S(n), S_cnt(n); loop_rev(i, n-1, 0) { if(sz(graph[i][0]) && sz(graph[i][1])) { int x = graph[i][0][0], y = graph[i][1][0]; int l = lca(x, y); S[x] += S[i] + 1, S[y] += S[i] + 1; if(l != (-1)) S[l] -= (S[i] + 1); } else { for(int s : graph[i][0]) S[s] += S[i] + 1; for(int s : graph[i][1]) S[s] += S[i] + 1; } } loop(i, 0, n-1) ++S_cnt[S[i]]; ll res = 0; auto c = [&](int nn, int kk) -> ll { return mul(mul(fact[nn], fact_inv[nn - kk]), fact_inv[kk]); }; auto f = [&](int S_val) -> ll { return mul(mul(c(n, S_val + 1), fact[S_val]), fact[n - S_val - 1]); }; loop(S_val, 0, n-1) { res = add(res, mul(S_cnt[S_val], f(S_val))); } pint(mul(res, qpow(fact[n], MOD-2))), putchar_unlocked('\n'); }
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 | #include <bits/stdc++.h> #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using namespace std; __always_inline int rint() { static int res; static char c; res = 0; do { c = getchar_unlocked(); } while(!isdigit(c)); while(isdigit(c)) { res = 10 * res + c - '0', c = getchar_unlocked(); } return res; } __always_inline void pint(int x) { static int ptr; static char buff[20]; ptr = 0; do { buff[ptr++] = '0' + x % 10, x /= 10; } while(x); while(ptr) { putchar_unlocked(buff[--ptr]); } } #pragma GCC maksuje_zadania_na_essie("pot200"); #define loop(i, a, b) for(int i = a; i <= b; i++) #define loop_rev(i, a, b) for(int i = a; i >= b; i--) #define all(x) x.begin(), x.end() #define sz(x) int(x.size()) #define pb push_back using ll = int64_t; using ull = uint64_t; using uint = uint32_t; struct Shelf { int x1, x2, y; }; constexpr ll MOD = 1e9 + 7; ll mul(ll a, ll b) { return (a * b % MOD); } ll add(ll a, ll b) { return (a + b >= MOD ? a + b - MOD : a + b); } ll sub(ll a, ll b) { return (a - b < 0 ? a - b + MOD : a - b); } ll qpow(ll a, ll b) { ll res = 1; while(b) { if(b&1) res = mul(res, a); a = mul(a, a); b /= 2; } return res; } constexpr int MAX_N = 5e5 + 1; ll fact_inv[MAX_N]; ll fact[MAX_N]; constexpr int LOG = 19; int jmp[MAX_N][2][LOG]; int depth[MAX_N][2]; Shelf shelves[MAX_N]; int lg; int lift(int x, int h, int type) { int i = 0; while(h > 0) { if(x == (-1)) return (-1); if(h&1) { x = jmp[x][type][i]; } h /= 2; ++i; } return x; } int first_greater_end(int v, int x) { if(shelves[v].x2 > x) return v; loop_rev(i, lg-1, 0) { int new_v = jmp[v][1][i]; if(new_v != (-1) && shelves[new_v].x2 <= x) { v = new_v; } } return jmp[v][1][0]; } int first_smaller_start(int v, int x) { if(shelves[v].x1 < x) return v; loop_rev(i, lg-1, 0) { int new_v = jmp[v][0][i]; if(new_v != (-1) && shelves[new_v].x1 >= x) { v = new_v; } } return jmp[v][0][0]; } int lift_to(int v, int type, int dest) { int lifted = lift(v, depth[v][type] - depth[dest][type], type); if(lifted == dest) return dest; else return (-1); } int lca(int a, int b) { if(a == b) return a; if(b > a) { int l = 0, r = depth[b][0]; while(l < r) { int mid = (l+r)/2; int b_lifted = lift(b, mid, 0); int a_lifted = first_greater_end(a, shelves[b_lifted].x1); if(a_lifted == (-1) || shelves[a_lifted].y < shelves[b_lifted].y) { l = mid + 1; } else { r = mid; } } int final_b_lifted = lift(b, l, 0); int final_a_lifted = lift_to(a, 1, final_b_lifted); if(final_b_lifted == final_a_lifted) return final_a_lifted; } else { int l = 0, r = depth[a][1]; while(l < r) { int mid = (l+r)/2; int a_lifted = lift(a, mid, 1); int b_lifted = first_smaller_start(b, shelves[a_lifted].x2); if(b_lifted == (-1) || shelves[b_lifted].y < shelves[a_lifted].y) { l = mid + 1; } else { r = mid; } } int final_a_lifted = lift(a, l, 1); int final_b_lifted = lift_to(b, 0, final_a_lifted); if(final_a_lifted == final_b_lifted) return final_a_lifted; } return (-1); } int main() { cin.tie(0)->sync_with_stdio(false); int n = rint(); lg = int(log2(n)) + 1; vector<vector<vector<int>>> graph(n, vector<vector<int>>(2)); loop(i, 0, n-1) { loop(j, 0, LOG-1) { jmp[i][0][j] = jmp[i][1][j] = (-1); } } fact[0] = 1; loop(i, 1, n) fact[i] = mul(fact[i-1], i); fact_inv[n] = qpow(fact[n], MOD-2); loop_rev(i, n, 1) fact_inv[i-1] = mul(i, fact_inv[i]); loop(i, 0, n-1) { shelves[i].x1 = rint(); shelves[i].x2 = rint(); shelves[i].y = i; } set<tuple<int,int,int>> open; loop_rev(i, n-1, 0) { if(!open.empty()) { auto it = open.upper_bound({ shelves[i].x1, -1, -1 }); while(it != open.end() && get<0>(*it) < shelves[i].x2) { graph[get<1>(*it)][get<2>(*it)].pb(i); it = open.erase(it); } } open.emplace(shelves[i].x1, i, 0); open.emplace(shelves[i].x2, i, 1); } loop(i, 0, n-1) { loop(type, 0, 1) { jmp[i][type][0] = (-1); for(int s : graph[i][type]) { // cause it can be empty (jajo edge case) jmp[i][type][0] = s; loop(len, 1, lg-1) { if(jmp[i][type][len-1] != (-1)) { jmp[i][type][len] = jmp[jmp[i][type][len-1]][type][len-1]; } } } } } loop(i, 0, n-1) { loop(type, 0, 1) { if(graph[i][type].empty()) depth[i][type] = 0; else depth[i][type] = depth[graph[i][type][0]][type] + 1; } } vector<int> S(n), S_cnt(n); loop_rev(i, n-1, 0) { if(sz(graph[i][0]) && sz(graph[i][1])) { int x = graph[i][0][0], y = graph[i][1][0]; int l = lca(x, y); S[x] += S[i] + 1, S[y] += S[i] + 1; if(l != (-1)) S[l] -= (S[i] + 1); } else { for(int s : graph[i][0]) S[s] += S[i] + 1; for(int s : graph[i][1]) S[s] += S[i] + 1; } } loop(i, 0, n-1) ++S_cnt[S[i]]; ll res = 0; auto c = [&](int nn, int kk) -> ll { return mul(mul(fact[nn], fact_inv[nn - kk]), fact_inv[kk]); }; auto f = [&](int S_val) -> ll { return mul(mul(c(n, S_val + 1), fact[S_val]), fact[n - S_val - 1]); }; loop(S_val, 0, n-1) { res = add(res, mul(S_cnt[S_val], f(S_val))); } pint(mul(res, qpow(fact[n], MOD-2))), putchar_unlocked('\n'); } |