#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
using namespace __gnu_pbds;
using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const ll I = 1000LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL;
const ll M = 1000LL * 1000LL * 1000LL + 7LL;
const int N = 500 * 1000 + 1;
ll sil[N], osil[N];
int il[N];
ull dp[N];
vector<int> ed[N];
set<pair<int, int>> curl;
pair<int, int> tab[N];
set<pair<int, int>>::iterator it;
ll QP(ll a, ll n)
{
ll ans = 1LL;
while(n > 0LL)
{
if(n % 2LL == 1LL) ans = (ans * a) % M;
a = (a * a) % M;
n /= 2LL;
}
return ans;
}
void PreSil(int n)
{
sil[0] = 1LL;
for(int i = 1; i <= n; ++i) sil[i] = (sil[i - 1] * (ll)i) % M;
osil[n] = QP(sil[n], M - 2LL);
for(int i = n - 1; i >= 0; --i) osil[i] = (osil[i + 1] * (ll)(i + 1)) % M;
}
inline ll NK(int n, int k)
{
return (((sil[n] * osil[k]) % M) * osil[n - k]) % M;
}
ll Cnt(int n, int k)
{
ll ans = NK(n, k + 1);
ans *= (sil[k] * sil[n - k - 1]) % M;
ans %= M;
return ans;
}
void GenIN(int n)
{
srand(clock());
for(int i = 1; i <= n; ++i)
{
int a = rand() % (2 * n) + 1, b = rand() % (2 * n) + 1;
tab[i].st = min(a, b);
tab[i].nd = max(a, b);
}
}
void CntIL(int n)
{
int s;
for(int l = 0; l < (n + 63) / 64; ++l)
{
s = l * 64 + 1;
for(int i = s; i < s + 64; ++i)
dp[i] = ((ull)1<<(ull)(i - s));
for(int i = s; i <= n; ++i)
{
il[i] += __builtin_popcountll(dp[i]);
for(int j = 0; j < (int)ed[i].size(); ++j)
dp[ed[i][j]] |= dp[i];
dp[i] = 0;
}
}
}
void Solve()
{
int n; ll ans = 0;
cin >> n;
//n = 100;
//GenIN(n);
PreSil(n);
for(int i = 1; i <= n; ++i)
cin >> tab[i].st >> tab[i].nd;
reverse(tab + 1, tab + 1 + n);
for(int i = 1; i <= n; ++i)
{
it = curl.lower_bound(make_pair(tab[i].st, 0));
while(it != curl.end() && (*it).st <= tab[i].nd)
{
ed[(*it).nd].pb(i);
curl.erase(it);
it = curl.lower_bound(make_pair(tab[i].st, 0));
}
curl.insert(make_pair(tab[i].st, i));
curl.insert(make_pair(tab[i].nd, i));
}
CntIL(n);
for(int i = 1; i <= n; ++i)
ans += Cnt(n, il[i] - 1);
ans %= M;
ans *= osil[n];
cout << ans % M << "\n";
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
//int t; cin >> t;
//while(t--)
Solve();
return 0;
}
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 | #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update> using namespace __gnu_pbds; using namespace std; #define pb push_back #define st first #define nd second typedef long long ll; typedef unsigned long long ull; typedef long double ld; const ll I = 1000LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL; const ll M = 1000LL * 1000LL * 1000LL + 7LL; const int N = 500 * 1000 + 1; ll sil[N], osil[N]; int il[N]; ull dp[N]; vector<int> ed[N]; set<pair<int, int>> curl; pair<int, int> tab[N]; set<pair<int, int>>::iterator it; ll QP(ll a, ll n) { ll ans = 1LL; while(n > 0LL) { if(n % 2LL == 1LL) ans = (ans * a) % M; a = (a * a) % M; n /= 2LL; } return ans; } void PreSil(int n) { sil[0] = 1LL; for(int i = 1; i <= n; ++i) sil[i] = (sil[i - 1] * (ll)i) % M; osil[n] = QP(sil[n], M - 2LL); for(int i = n - 1; i >= 0; --i) osil[i] = (osil[i + 1] * (ll)(i + 1)) % M; } inline ll NK(int n, int k) { return (((sil[n] * osil[k]) % M) * osil[n - k]) % M; } ll Cnt(int n, int k) { ll ans = NK(n, k + 1); ans *= (sil[k] * sil[n - k - 1]) % M; ans %= M; return ans; } void GenIN(int n) { srand(clock()); for(int i = 1; i <= n; ++i) { int a = rand() % (2 * n) + 1, b = rand() % (2 * n) + 1; tab[i].st = min(a, b); tab[i].nd = max(a, b); } } void CntIL(int n) { int s; for(int l = 0; l < (n + 63) / 64; ++l) { s = l * 64 + 1; for(int i = s; i < s + 64; ++i) dp[i] = ((ull)1<<(ull)(i - s)); for(int i = s; i <= n; ++i) { il[i] += __builtin_popcountll(dp[i]); for(int j = 0; j < (int)ed[i].size(); ++j) dp[ed[i][j]] |= dp[i]; dp[i] = 0; } } } void Solve() { int n; ll ans = 0; cin >> n; //n = 100; //GenIN(n); PreSil(n); for(int i = 1; i <= n; ++i) cin >> tab[i].st >> tab[i].nd; reverse(tab + 1, tab + 1 + n); for(int i = 1; i <= n; ++i) { it = curl.lower_bound(make_pair(tab[i].st, 0)); while(it != curl.end() && (*it).st <= tab[i].nd) { ed[(*it).nd].pb(i); curl.erase(it); it = curl.lower_bound(make_pair(tab[i].st, 0)); } curl.insert(make_pair(tab[i].st, i)); curl.insert(make_pair(tab[i].nd, i)); } CntIL(n); for(int i = 1; i <= n; ++i) ans += Cnt(n, il[i] - 1); ans %= M; ans *= osil[n]; cout << ans % M << "\n"; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); //int t; cin >> t; //while(t--) Solve(); return 0; } |
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