結果
| 問題 | No.2873 Kendall's Tau |
| ユーザー |
 maspy
|
| 提出日時 | 2024-09-09 22:27:59 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 515 ms / 4,500 ms |
| コード長 | 29,214 bytes |
| コンパイル時間 | 5,378 ms |
| コンパイル使用メモリ | 331,644 KB |
| 実行使用メモリ | 13,396 KB |
| 最終ジャッジ日時 | 2024-09-09 22:28:16 |
| 合計ジャッジ時間 | 14,644 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,944 KB |
| testcase_02 | AC | 2 ms
6,944 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 1 ms
6,940 KB |
| testcase_05 | AC | 2 ms
6,940 KB |
| testcase_06 | AC | 1 ms
6,944 KB |
| testcase_07 | AC | 483 ms
13,140 KB |
| testcase_08 | AC | 501 ms
13,396 KB |
| testcase_09 | AC | 515 ms
13,268 KB |
| testcase_10 | AC | 506 ms
13,396 KB |
| testcase_11 | AC | 504 ms
13,268 KB |
| testcase_12 | AC | 480 ms
13,168 KB |
| testcase_13 | AC | 135 ms
6,940 KB |
| testcase_14 | AC | 407 ms
11,444 KB |
| testcase_15 | AC | 74 ms
6,940 KB |
| testcase_16 | AC | 75 ms
6,940 KB |
| testcase_17 | AC | 351 ms
10,712 KB |
| testcase_18 | AC | 246 ms
8,964 KB |
| testcase_19 | AC | 333 ms
10,412 KB |
| testcase_20 | AC | 84 ms
6,940 KB |
| testcase_21 | AC | 289 ms
9,464 KB |
| testcase_22 | AC | 110 ms
6,944 KB |
| testcase_23 | AC | 285 ms
9,620 KB |
| testcase_24 | AC | 32 ms
6,940 KB |
| testcase_25 | AC | 64 ms
6,944 KB |
| testcase_26 | AC | 368 ms
10,712 KB |
| testcase_27 | AC | 203 ms
8,136 KB |
| testcase_28 | AC | 393 ms
11,540 KB |
| testcase_29 | AC | 427 ms
12,460 KB |
| testcase_30 | AC | 51 ms
6,940 KB |
| testcase_31 | AC | 113 ms
6,944 KB |
| testcase_32 | AC | 286 ms
9,432 KB |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 1 "/home/maspy/compro/library/ds/bit_vector.hpp"
struct Bit_Vector {
int n;
bool prepared = 0;
vc<pair<u64, u32>> dat;
Bit_Vector(int n) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
void set(int i) {
assert(!prepared);
dat[i >> 6].fi |= u64(1) << (i & 63);
}
void reset() {
fill(all(dat), pair<u64, u32>{0, 0});
prepared = 0;
}
void build() {
prepared = 1;
FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
}
// [0, k) 内の 1 の個数
bool operator[](int i) { return dat[i >> 6].fi >> (i & 63) & 1; }
int count_prefix(int k, bool f = true) {
assert(prepared);
auto [a, b] = dat[k >> 6];
int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
return (f ? ret : k - ret);
}
int count(int L, int R, bool f = true) { return count_prefix(R, f) - count_prefix(L, f); }
string to_string() {
string ans;
FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
return ans;
}
};
#line 1 "/home/maspy/compro/library/ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
static_assert(is_same_v<T, int>);
int mi, ma;
vc<int> dat;
vc<int> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x: X) dat[x - mi + 1]++;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x: X) { x = dat[x - mi]++; }
FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
dat[0] = 0;
return X;
}
int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};
template <typename T>
struct Index_Compression_SAME_SMALL {
static_assert(is_same_v<T, int>);
int mi, ma;
vc<int> dat;
vc<int> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x: X) dat[x - mi + 1] = 1;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x: X) { x = dat[x - mi]; }
return X;
}
int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};
template <typename T>
struct Index_Compression_SAME_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
vc<int> I = argsort(X);
vc<int> res(len(X));
for (auto& i: I) {
if (!dat.empty() && dat.back() == X[i]) {
res[i] = len(dat) - 1;
} else {
res[i] = len(dat);
dat.eb(X[i]);
}
}
dat.shrink_to_fit();
return res;
}
int operator()(T x) { return LB(dat, x); }
};
template <typename T>
struct Index_Compression_DISTINCT_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
vc<int> I = argsort(X);
vc<int> res(len(X));
for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); }
dat.shrink_to_fit();
return res;
}
int operator()(T x) { return LB(dat, x); }
};
template <typename T, bool SMALL>
using Index_Compression_DISTINCT =
typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>,
Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME =
typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>,
Index_Compression_SAME_LARGE<T>>::type;
// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression =
typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>,
Index_Compression_DISTINCT<T, SMALL>>::type;
#line 2 "/home/maspy/compro/library/alg/monoid/add.hpp"
template <typename E>
struct Monoid_Add {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 4 "/home/maspy/compro/library/ds/wavelet_matrix/wavelet_matrix.hpp"
// 静的メソッドinverseの存在をチェックするテンプレート
template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};
template <typename T>
struct has_inverse<T, std::void_t<decltype(
T::inverse(std::declval<typename T::value_type>()))>>
: std::true_type {};
struct Dummy_Data_Structure {
using MX = Monoid_Add<bool>;
void build(const vc<bool>& A) {}
};
template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
int n, log, K;
Index_Compression<Y, true, SMALL_Y> IDX;
vc<Y> ItoY;
vc<int> mid;
vc<Bit_Vector> bv;
vc<SEGTREE> seg;
Wavelet_Matrix() {}
Wavelet_Matrix(const vc<Y>& A) { build(A); }
Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
template <typename F>
Wavelet_Matrix(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
vc<Y> A(m);
vc<T> S(m);
for (int i = 0; i < m; ++i) tie(A[i], S[i]) = f(i);
build(A, S);
}
void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
void build(const vc<Y>& A, vc<T> S) {
n = len(A);
vc<int> B = IDX.build(A);
K = 0;
for (auto& x: B) chmax(K, x + 1);
ItoY.resize(K);
FOR(i, n) ItoY[B[i]] = A[i];
log = 0;
while ((1 << log) < K) ++log;
mid.resize(log), bv.assign(log, Bit_Vector(n));
vc<int> B0(n), B1(n);
vc<T> S0(n), S1(n);
seg.resize(log + 1);
seg[log].build(S);
for (int d = log - 1; d >= 0; --d) {
int p0 = 0, p1 = 0;
for (int i = 0; i < n; ++i) {
bool f = (B[i] >> d & 1);
if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
}
swap(B, B0), swap(S, S0);
move(B1.begin(), B1.begin() + p1, B.begin() + p0);
move(S1.begin(), S1.begin() + p1, S.begin() + p0);
mid[d] = p0, bv[d].build(), seg[d].build(S);
}
}
// [L,R) x [0,y)
int prefix_count(int L, int R, Y y) {
int p = IDX(y);
if (L == R || p == 0) return 0;
if (p == K) return R - L;
int cnt = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
if (!(p >> d & 1)) L = l0, R = r0;
}
return cnt;
}
// [L,R) x [y1,y2)
int count(int L, int R, Y y1, Y y2) {
return prefix_count(L, R, y2) - prefix_count(L, R, y1);
}
// [L,R) x [0,y)
pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
int p = IDX(y);
if (p == 0) return {0, Mono::unit()};
if (p == K) return {R - L, seg[log].prod(L, R)};
int cnt = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (p >> d & 1) {
cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1;
}
if (!(p >> d & 1)) L = l0, R = r0;
}
return {cnt, t};
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
if constexpr (has_inverse<Mono>::value) {
auto [c1, t1] = prefix_count_and_prod(L, R, y1);
auto [c2, t2] = prefix_count_and_prod(L, R, y2);
return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
}
int lo = IDX(y1), hi = IDX(y2), cnt = 0;
T t = Mono::unit();
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
assert(b - a == (1 << d));
if (hi <= a || b <= lo) return;
if (lo <= a && b <= hi) {
cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return {cnt, t};
}
// [L,R) x [y1,y2)
T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
// [L,R) x [y1,y2)
T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }
T prod_all(int L, int R) { return seg[log].prod(L, R); }
Y kth(int L, int R, int k) {
assert(0 <= k && k < R - L);
int p = 0;
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
}
}
return ItoY[p];
}
// y 以上最小 OR infty<Y>
Y next(int L, int R, Y y) {
int k = IDX(y);
int p = K;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (p <= a || L == R || b <= k) return;
if (d == 0) {
chmin(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == K ? infty<Y> : ItoY[p]);
}
// y 以下最大 OR -infty<T>
Y prev(int L, int R, Y y) {
int k = IDX(y + 1);
int p = -1;
auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
if (b - 1 <= p || L == R || k <= a) return;
if (d == 0) {
chmax(p, a);
return;
}
--d;
int c = (a + b) / 2;
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
};
dfs(dfs, log, L, R, 0, 1 << log);
return (p == -1 ? -infty<Y> : ItoY[p]);
}
Y median(bool UPPER, int L, int R) {
assert(0 <= L && L < R && R <= n);
int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
return kth(L, R, k);
}
pair<Y, T> kth_value_and_prod(int L, int R, int k) {
assert(0 <= k && k <= R - L);
if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
int p = 0;
T t = Mono::unit();
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (k < r0 - l0) {
L = l0, R = r0;
} else {
t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1,
p |= 1 << d;
}
}
t = Mono::op(t, seg[0].prod(L, L + k));
return {ItoY[p], t};
}
T prod_index_range(int L, int R, int k1, int k2) {
static_assert(has_inverse<Mono>::value);
T t1 = kth_value_and_prod(L, R, k1).se;
T t2 = kth_value_and_prod(L, R, k2).se;
return Mono::op(Mono::inverse(t1), t2);
}
// [L,R) x [0,y) での check(cnt, prod) が true となる最大の (cnt,prod)
template <typename F>
pair<int, T> max_right(F check, int L, int R) {
int cnt = 0;
T t = Mono::unit();
assert(check(0, Mono::unit()));
if (check(R - L, seg[log].prod(L, R))) {
return {R - L, seg[log].prod(L, R)};
}
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
int cnt1 = cnt + r0 - l0;
T t1 = Mono::op(t, seg[d].prod(l0, r0));
if (check(cnt1, t1)) {
cnt = cnt1, t = t1, L = l1, R = r1;
} else {
L = l0, R = r0;
}
}
return {cnt, t};
}
void set(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].set(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].set(L, t);
}
}
void multiply(int i, T t) {
assert(0 <= i && i < n);
int L = i, R = i + 1;
seg[log].multiply(L, t);
for (int d = log - 1; d >= 0; --d) {
int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
if (l0 < r0) L = l0, R = r0;
if (l0 == r0) L = l1, R = r1;
seg[d].multiply(L, t);
}
}
};
#line 2 "/home/maspy/compro/library/ds/wavelet_matrix/wavelet_matrix_2d_range.hpp"
template <typename XY, bool SMALL_X, bool SMALL_Y,
typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix_2D_Range {
// 点群を X 昇順に並べる.
Wavelet_Matrix<XY, SMALL_Y, SEGTREE> WM;
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
Index_Compression<XY, false, SMALL_X> IDX_X;
int n;
vc<int> new_idx;
template <typename F>
Wavelet_Matrix_2D_Range(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
n = m;
vc<XY> X(n), Y(n);
vc<T> S(n);
FOR(i, n) {
auto tmp = f(i);
X[i] = get<0>(tmp), Y[i] = get<1>(tmp), S[i] = get<2>(tmp);
}
new_idx = IDX_X.build(X);
vc<int> I(n);
FOR(i, n) I[new_idx[i]] = i;
Y = rearrange(Y, I);
S = rearrange(S, I);
WM.build(Y, S);
}
int count(XY x1, XY x2, XY y1, XY y2) {
return WM.count(IDX_X(x1), IDX_X(x2), y1, y2);
}
// [L,R) x [-inf,y)
pair<int, T> prefix_count_and_prod(XY x1, XY x2, XY y) {
return WM.prefix_count_and_prod(IDX_X(x1), IDX_X(x2), y);
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(XY x1, XY x2, XY y1, XY y2) {
return WM.count_and_prod(IDX_X(x1), IDX_X(x2), y1, y2);
}
// [L,R) x [-inf,inf)
T prod_all(XY x1, XY x2) { return WM.prod_all(IDX_X(x1), IDX_X(x2)); }
// [L,R) x [-inf,y)
T prefix_prod(XY x1, XY x2, XY y) {
return WM.prefix_prod(IDX_X(x1), IDX_X(x2), y);
}
// [L,R) x [y1,y2)
T prod(XY x1, XY x2, XY y1, XY y2) {
return WM.prod(IDX_X(x1), IDX_X(x2), y1, y2);
}
// [L,R) x [-inf,y) での check(cnt, prod) が true となる最大の (cnt,prod)
template <typename F>
pair<int, T> max_right(F check, XY x1, XY x2) {
return WM.max_right(check, IDX_X(x1), IDX_X(x2));
}
// i は最初に渡したインデックス
void set(int i, T t) { WM.set(new_idx[i], t); }
// i は最初に渡したインデックス
void multiply(int i, T t) { WM.multiply(new_idx[i], t); }
};
#line 2 "/home/maspy/compro/library/ds/static_range_product_group.hpp"
template <typename Monoid>
struct Static_Range_Product_Group {
using MX = Monoid;
using X = typename MX::value_type;
int n;
vc<X> dat;
Static_Range_Product_Group() {}
template <typename F>
Static_Range_Product_Group(int m, F f) {
build(m, f);
}
template <typename F>
void build(int m, F f) {
n = m;
dat.assign(n + 1, MX::unit());
for (int i = 0; i < n; ++i) dat[i + 1] = MX::op(dat[i], f(i));
}
void build(vc<X>& A) {
n = len(A);
dat.assign(n + 1, MX::unit());
for (int i = 0; i < n; ++i) dat[i + 1] = MX::op(dat[i], A[i]);
}
X prod(int l, int r) { return MX::op(MX::inverse(dat[l]), dat[r]); }
};
template <typename T>
using Prefix_Sum = Static_Range_Product_Group<Monoid_Add<T>>;
#line 6 "main.cpp"
void solve() {
LL(N);
vc<int> X(N), Y(N);
FOR(i, N) read(X[i], Y[i]);
Wavelet_Matrix_2D_Range<int, false, false> WM(N, [&](int i) -> tuple<int, int, int> { return {X[i], Y[i], 1}; });
ll P = 0, Q = 0, R = 0, S = 0;
FOR(i, N) {
R += WM.count(-infty<int>, X[i], -infty<int>, infty<int>);
S += WM.count(-infty<int>, infty<int>, -infty<int>, Y[i]);
P += WM.count(-infty<int>, X[i], -infty<int>, Y[i]);
Q += WM.count(-infty<int>, X[i], Y[i] + 1, infty<int>);
}
double ANS;
ANS = P - Q;
ANS /= sqrtl(double(R) * S);
print(ANS);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}