結果
| 問題 | No.2873 Kendall's Tau |
| ユーザー |
 T101010101
|
| 提出日時 | 2024-09-09 00:45:51 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 32,203 bytes |
| コンパイル時間 | 11,293 ms |
| コンパイル使用メモリ | 368,552 KB |
| 実行使用メモリ | 126,812 KB |
| 最終ジャッジ日時 | 2024-09-09 00:46:40 |
| 合計ジャッジ時間 | 47,701 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
6,816 KB |
| testcase_01 | AC | 2 ms
6,944 KB |
| testcase_02 | AC | 2 ms
6,944 KB |
| testcase_03 | AC | 2 ms
6,944 KB |
| testcase_04 | AC | 2 ms
6,940 KB |
| testcase_05 | AC | 2 ms
6,944 KB |
| testcase_06 | AC | 2 ms
6,944 KB |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | AC | 641 ms
42,244 KB |
| testcase_14 | WA | - |
| testcase_15 | AC | 336 ms
25,808 KB |
| testcase_16 | AC | 352 ms
27,144 KB |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | AC | 351 ms
26,828 KB |
| testcase_21 | WA | - |
| testcase_22 | AC | 557 ms
35,444 KB |
| testcase_23 | WA | - |
| testcase_24 | AC | 151 ms
14,592 KB |
| testcase_25 | AC | 313 ms
25,068 KB |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | AC | 243 ms
19,676 KB |
| testcase_31 | AC | 506 ms
34,672 KB |
| testcase_32 | WA | - |
ソースコード
#pragma region Macros
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2,popcnt")
#include <bits/extc++.h>
#include <atcoder/all>
using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<256>>;
// Bdouble Beps = 0.00000000000000000000000000000001; // 1e-32
// const bool equals(Bdouble a, Bdouble b) { return mp::fabs(a - b) < Beps; }
#define pb emplace_back
#define int ll
#define endl '\n'
#define sqrt __builtin_sqrtl
#define cbrt __builtin_cbrtl
#define hypot __builtin_hypotl
// #define next asdnext
// #define prev asdprev
using ll = long long;
using ld = long double;
const ld PI = acosl(-1);
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
const int MOD = 998244353;
// const int MOD = 1000000007;
const ld EPS = 1e-10;
const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; }
const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1};
#define EC int
struct Edge {
int from, to;
EC cost;
Edge() : from(-1), to(-1), cost(-1) {}
Edge(int to, EC cost) : to(to), cost(cost) {}
Edge(int from, int to, EC cost) : from(from), to(to), cost(cost) {}
bool operator ==(const Edge& e) {
return this->from == e.from && this->to == e.to && this->cost == e.cost;
}
bool operator !=(const Edge& e) {
return this->from != e.from or this->to != e.to or this->cost != e.cost;
}
bool operator <(const Edge& e) { return this->cost < e.cost; }
bool operator >(const Edge& e) { return this->cost > e.cost; }
};
chrono::system_clock::time_point start;
__attribute__((constructor))
void constructor() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(10);
start = chrono::system_clock::now();
}
random_device seed_gen;
mt19937_64 rng(seed_gen());
uniform_int_distribution<int> dist_x(0, 1e9);
struct RNG {
unsigned Int() {
return dist_x(rng);
}
unsigned Int(unsigned l, unsigned r) {
return dist_x(rng) % (r - l + 1) + l;
}
ld Double() {
return ld(dist_x(rng)) / 1e9;
}
} rnd;
namespace bit_function {
using i64 = ll;
// using i64 = uint64_t;
// bit演算, x==0の場合は例外処理した方がよさそう. 区間は [l, r)
i64 lrmask(int l, int r) { return (1LL << r) - (1LL << l); }
i64 sub_bit(i64 x, int l, int r) { i64 b = x & ((1LL << r) - (1LL << l)); return b >> l; } // r溢れ可
i64 bit_width(i64 x) { return 64 - __builtin_clzll(x) + (x == 0); }
i64 popcount(i64 x) { return __builtin_popcountll(x); }
i64 popcount(i64 x, int l, int r) { return __builtin_popcountll(sub_bit(x, l, r)); }
i64 unpopcount(i64 x) { return bit_width(x) - __builtin_popcountll(x); } // 最上位bitより下のみ
i64 unpopcount(i64 x, int l, int r) { return r - l - __builtin_popcountll(sub_bit(x, l, r)); } // 最上位bitより上も含まれうる
bool is_pow2(i64 x) { return __builtin_popcountll(x) == 1; } // xが負のときは常にfalse
bool is_pow4(i64 x) { return __builtin_popcountll(x) == 1 && __builtin_ctz(x) % 2 == 0; }
//bool is_pow4(ll x) { return __builtin_popcountll(x) == 1 && (x&0x55555555); }
int top_bit(i64 x) { return 63 - __builtin_clzll(x);} // 2^kの位 (x > 0)
int bot_bit(i64 x) { return __builtin_ctzll(x);} // 2^kの位 (x > 0)
int next_bit(i64 x, int k) { // upper_bound
x >>= (k + 1);
int pos = k + 1;
while (x > 0) {
if (x & 1) return pos;
x >>= 1;
pos++;
}
return -1;
}
int prev_bit(i64 x, int k) {
// k = min(k, bit_width(x)); ?
int pos = 0;
while (x > 0 && pos < k) {
if (x & 1) {
if (pos < k) return pos;
}
x >>= 1;
pos++;
}
return -1;
}
int kth_bit(i64 x, int k) { // kは1-indexed
int pos = 0, cnt = 0;
while (x > 0) {
if (x & 1) {
cnt++;
if (cnt == k) return pos;
}
x >>= 1;
pos++;
}
return -1;
}
i64 msb(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // mask
i64 lsb(i64 x) { return (x & -x); } // mask
int countl_zero(i64 x) { return __builtin_clzll(x); }
int countl_one(i64 x) { // countl_oneと定義が異なるので注意
i64 ret = 0, k = 63 - __builtin_clzll(x);
while (k != -1 && (x & (1LL << k))) { k--; ret++; }
return ret;
}
int countr_zero(i64 x) { return __builtin_ctzll(x); } // x=0のとき64
int countr_one(i64 x) { int ret = 0; while (x & 1) { x >>= 1; ret++; } return ret; }
// int countr_one(ll x) { return __builtin_popcount(x ^ (x & -~x));
i64 l_one(i64 x) { // 最上位で連なってる1のmask
if (x == 0) return 0;
i64 ret = 0, k = 63 - __builtin_clzll(x);
while (k != -1 && (x & (1LL << k))) { ret += 1LL << k; k--; }
return ret;
}
int floor_log2(i64 x) { return 63 - __builtin_clzll(x); } // top_bit
int ceil_log2(i64 x) { return 64 - __builtin_clzll(x - 1); }
i64 bit_floor(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // msb
i64 bit_ceil(i64 x) { if (x == 0) return 0; return 1LL << (64 - __builtin_clzll(x - 1)); }
i64 rotl(i64 x, int k) { // 有効bit内でrotate. オーバーフロー注意
i64 w = bit_width(x); k %= w;
return ((x << k) | (x >> (w - k))) & ((1LL << w) - 1);
}
// i64 rotl(i64 x, i64 l, i64 m, i64 r) {}
i64 rotr(i64 x, int k) {
i64 w = bit_width(x); k %= w;
return ((x >> k) | (x << (w - k))) & ((1LL << w) - 1);
}
// i64 rotr(i64 x, i64 l, i64 m, i64 r) {}
i64 bit_reverse(i64 x) { // 有効bit内で左右反転
i64 r = 0, w = bit_width(x);
for (i64 i = 0; i < w; i++) r |= ((x >> i) & 1) << (w - i - 1);
return r;
}
// i64 bit_reverse(i64 x, int l, int r) {}
bool is_palindrome(i64 x) { return x == bit_reverse(x); }
bool is_palindrome(i64 x, int l, int r) { i64 b = sub_bit(x, l, r); return b == bit_reverse(b); }
i64 concat(i64 a, i64 b) { return (a << bit_width(b)) | b; } // オーバーフロー注意
i64 erase(i64 x, int l, int r) { return x >> r << l | x & ((1LL << l) - 1); } // [l, r) をカット
i64 hamming(i64 a, i64 b) { return __builtin_popcountll(a ^ b); }
i64 hamming(i64 a, i64 b, int l, int r) { return __builtin_popcountll(sub_bit(a, l, r) ^ sub_bit(b, l, r)); }
i64 compcount(i64 x) { return (__builtin_popcountll(x ^ (x >> 1)) + (x & 1)) / 2; }
i64 compcount2(i64 x) { return compcount(x & (x >> 1)); } // 長さ2以上の連結成分の個数
i64 adjacount(i64 x) { return __builtin_popcountll(x & (x >> 1)); } // 隣接する1のペアの個数
i64 next_combination(i64 x) {
i64 t = x | (x - 1); return (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctzll(x) + 1));
}
} using namespace bit_function;
namespace util_function {
namespace Std = std;
__int128_t POW(__int128_t x, int n) {
__int128_t ret = 1;
assert(n >= 0);
if (x == 1 or n == 0) ret = 1;
else if (x == -1 && n % 2 == 0) ret = 1;
else if (x == -1) ret = -1;
else if (n % 2 == 0) {
// assert(x < INFL);
ret = POW(x * x, n / 2);
} else {
// assert(x < INFL);
ret = x * POW(x, n - 1);
}
return ret;
}
int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq
assert(y != 0);
if (x >= 0 && y > 0) return x / y;
if (x >= 0 && y < 0) return x / y - (x % y < 0);
if (x < 0 && y < 0) return x / y + (x % y < 0);
return x / y - (x % y < 0); // (x < 0 && y > 0)
}
int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr
assert(y != 0);
return x - y * per(x, y);
} // https://yukicoder.me/problems/no/2781
int floor(int x, int y) { // (ld)x / y 以下の最大の整数
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x >= 0 ? x / y : (x + 1) / y - 1;
}
int ceil(int x, int y) { // (ld)x / y 以上の最小の整数
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x > 0 ? (x - 1) / y + 1 : x / y;
}
int round(int x, int y) { // (ld)(x/y)を小数点第1位について四捨五入
assert(y != 0);
return (x * 2 + y) / (y * 2);
}
int round(int x, int y, int k) { // (ld)(x/y)を10^kの位に関して四捨五入
assert(y != 0 && k >= 0);
if (k == 0) return (x * 2 + y) / (y * 2);
x /= y * POW(10, k - 1);
if (x % 10 >= 5) return (x + 10 - x % 10) * POW(10, k - 1);
return x * POW(10, k - 1);
}
int round2(int x, int y) { // 五捨五超入 // 未verify
assert(y != 0);
if (y < 0) y = -y, x = -x;
int z = x / y;
if ((z * 2 + 1) * y <= y * 2) z++;
return z;
}
ld round(ld x, int k) { // xを10^kの位に関して四捨五入. to_string(x, k)優先
// x += EPS;
ld d = pow(10, -k);
return Std::round(x * d) / d;
}
ld floor(ld x, int k) { // xを10^kの位に関してflooring
// x += EPS;
ld d = pow(10, -k);
return Std::floor(x * d) / d; // 未verify
}
ld ceil(ld x, int k) { // xを10^kの位に関してceiling
// x -= EPS;
ld d = pow(10, -k);
return Std::ceil(x * d) / d; // 未verify
}
// int kth(int x, int y, int k) { // x / yの10^kの位の桁
// }
int floor(ld x, ld y) { // 誤差対策TODO
assert(!equals(y, 0));
return Std::floor(x / y);
// floor(x) = ceil(x - 1) という話も
}
int ceil(ld x, ld y) { // 誤差対策TODO // ceil(p/q) = -floor(-(p/q))らしい
assert(!equals(y, 0));
return Std::ceil(x / y);
// ceil(x) = floor(x + 1)
}
int perl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす q
// 未verify. 誤差対策TODO. EPS外してもいいかも。
assert(!equals(y, 0));
if (x >= 0 && y > 0) return Std::floor(x / y)+EPS;
if (x >= 0 && y < 0) return -Std::floor(x / fabs(y));
if (x < 0 && y < 0) return Std::floor(x / y) + (x - Std::floor(x/y)*y < -EPS);
return Std::floor(x / y) - (x - Std::floor(x/y)*y < -EPS); // (x < 0 && y > 0)
}
ld modl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす r
// 未verify. 誤差対策TODO. -0.0が返りうる。
assert(!equals(y, 0));
if (x >= 0) return x - fabs(y)*fabs(per(x, y));
return x - fabs(y)*floor(x, fabs(y));
}
int seisuu(ld x) { return (int)x; } // 整数部分. 誤差対策TODO
int modf(ld x) {
if (x < 0) return ceill(x);
else return floorl(x);
}
// 正なら+EPS, 負なら-EPSしてから、文字列に直して小数点以下を捨てる?
int seisuu(int x, int y) {
assert(y != 0);
return x / y;
}
int seisuu(ld x, ld y) { // 誤差対策TODO
assert(!equals(y, 0));
return (int)(x / y);
}
int floor_log(int base, int x) {
assert(base >= 2);
int ret = 0, now = 1;
while (now <= x) {
now *= base;
if (now <= x) ret++;
}
return ret;
}
int ceil_log(int base, int x) {
assert(base >= 2);
int ret = 0, now = 1;
while (now < x) {
now *= base;
ret++;
}
return ret;
}
template <class T> pair<T, T> max(const pair<T, T> &a, const pair<T, T> &b) {
if (a.first > b.first or a.first == b.first && a.second > b.second) return a;
return b;
}
template <class T> pair<T, T> min(const pair<T, T> &a, const pair<T, T> &b) {
if (a.first < b.first or a.first == b.first && a.second < b.second) return a;
return b;
}
template <class T> bool chmax(T &a, const T& b) {
if (a < b) { a = b; return true; } return false;
}
template <class T> bool chmin(T &a, const T& b) {
if (a > b) { a = b; return true; } return false;
}
template <class T> T mid(T a, T b, T c) { // 誤差対策TODO
return a + b + c - Std::max({a, b, c}) - Std::min({a, b, c});
}
template <class T> void Sort(T &a, T &b, bool rev = false) {
if (rev == false) if (a > b) swap(a, b);
else if (b > a) swap(b, a);
}
template <typename T, typename... Args>
void Sort(T& a, T& b, T& c, Args&... args) {
vector<T> vec = {a, b, c, args...};
sort(vec.begin(), vec.end());
auto it = vec.begin();
a = *it++; b = *it++; c = *it++;
int dummy[] = { (args = *it++, 0)... };
static_cast<void>(dummy);
}
template <typename T, typename... Args>
void Sortr(T& a, T& b, T& c, Args&... args) {
vector<T> vec = {a, b, c, args...};
sort(vec.rbegin(), vec.rend());
auto it = vec.begin();
a = *it++; b = *it++; c = *it++;
int dummy[] = { (args = *it++, 0)... };
static_cast<void>(dummy);
}
istream &operator >>(istream &is, __int128_t& x) {
string S; is >> S;
__int128_t ret = 0;
int f = 1;
if (S[0] == '-') f = -1;
for (int i = 0; i < S.length(); i++)
if ('0' <= S[i] && S[i] <= '9')
ret = ret * 10 + S[i] - '0';
x = ret * f;
return (is);
}
ostream &operator <<(ostream &os, __int128_t x) {
ostream::sentry s(os);
if (s) {
__uint128_t tmp = x < 0 ? -x : x;
char buffer[128]; char *d = end(buffer);
do {
--d; *d = "0123456789"[tmp % 10]; tmp /= 10;
} while (tmp != 0);
if (x < 0) { --d; *d = '-'; }
int len = end(buffer) - d;
if (os.rdbuf()->sputn(d, len) != len) os.setstate(ios_base::badbit);
}
return os;
}
__int128_t stoll(string &S) {
__int128_t ret = 0; int f = 1;
if (S[0] == '-') f = -1;
for (int i = 0; i < S.length(); i++)
if ('0' <= S[i] && S[i] <= '9') ret = ret * 10 + S[i] - '0';
return ret * f;
}
__int128_t gcd(__int128_t a, __int128_t b) { return b ? gcd(b, a % b) : a; }
__int128_t lcm(__int128_t a, __int128_t b) {
return a / gcd(a, b) * b;
// lcmが__int128_tに収まる必要あり
}
string to_string(ld x, int k) { // xの小数第k位までをstring化する
assert(k >= 0);
stringstream ss;
ss << setprecision(k + 2) << x;
string s = ss.str();
if (s.find('.') == string::npos) s += '.';
int pos = s.find('.');
for (int i = 0; k >= (int)s.size() - 1 - pos; i++) s += '0';
s.pop_back();
if (s.back() == '.') s.pop_back();
return s;
// stringstream ss; // 第k+1位を四捨五入して第k位まで返す
// ss << setprecision(k + 1) << x;
// string s = ss.str();
// if (s.find('.') == string::npos) s += '.';
// int pos = s.find('.');
// for (int i = 0; k > (int)s.size() - 1 - pos; i++) s += '0';
// if (s.back() == '.') s.pop_back();
// return s;
}
string to_string(__int128_t x) {
string ret = "";
if (x < 0) { ret += "-"; x *= -1; }
while (x) { ret += (char)('0' + x % 10); x /= 10; }
reverse(ret.begin(), ret.end());
return ret;
}
string to_string(char c) { string s = ""; s += c; return s; }
} using namespace util_function;
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<class T> size_t HashCombine(const size_t seed,const T &v) {
return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
template<class T,class S> struct hash<pair<T,S>>{
size_t operator()(const pair<T,S> &keyval) const noexcept {
return HashCombine(hash<T>()(keyval.first), keyval.second);
}
};
template<class T> struct hash<vector<T>>{
size_t operator()(const vector<T> &keyval) const noexcept {
size_t s=0;
for (auto&& v: keyval) s=HashCombine(s,v);
return s;
}
};
template<int N> struct HashTupleCore{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
size_t s=HashTupleCore<N-1>()(keyval);
return HashCombine(s,get<N-1>(keyval));
}
};
template <> struct HashTupleCore<0>{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct hash<tuple<Args...>>{
size_t operator()(const tuple<Args...> &keyval) const noexcept {
return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
}
};
template<typename T>
class Compress { // 試験運用, バグったらTをintにする
public:
int sz = 0;
// gp_hash_table<T, int, custom_hash> Z;
// gp_hash_table<int, T, custom_hash> UZ;
unordered_map<T, int> Z; // 元の値 -> 圧縮した値
unordered_map<int, T> UZ; // 圧縮した値 -> 元の値
Compress() {}
Compress(const vector<T> &V, T base = 0) {
this->sz = base;
set<T> s(V.begin(), V.end());
for (T x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
Compress(const vector<T> &V1, const vector<T> &V2, T base = 0) {
this->sz = base;
vector<T> V3 = V2;
V3.insert(V3.end(), V1.begin(), V1.end());
set<T> s(V3.begin(), V3.end());
for (T x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
Compress(const vector<T> &V1, const vector<T> &V2, const vector<T> &V3, T base = 0) {
this->sz = base;
vector<T> V4 = V1;
V4.insert(V4.end(), V2.begin(), V2.end());
V4.insert(V4.end(), V3.begin(), V3.end());
set<T> s(V4.begin(), V4.end());
for (T x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
Compress(const vector<T> &V1, const vector<T> &V2,
const vector<T> &V3, const vector<T> &V4, T base = 0) {
this->sz = base;
vector<T> V5 = V1;
V5.insert(V5.end(), V2.begin(), V2.end());
V5.insert(V5.end(), V3.begin(), V3.end());
V5.insert(V5.end(), V4.begin(), V4.end());
set<T> s(V5.begin(), V5.end());
for (T x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
vector<int> zip(const vector<T> &V) {
vector<int> ret(V.size());
for (int i = 0; i < (int)V.size(); i++) {
ret[i] = Z[V[i]];
}
return ret;
}
vector<T> unzip(const vector<int> &V) {
vector<T> ret(V.size());
for (int i = 0; i < (int)V.size(); i++) {
ret[i] = UZ[V[i]];
}
return ret;
}
int size() { return sz; }
T encode(int x) { return Z[x]; }
int decode(T x) {
if (UZ.find(x) == UZ.end()) return -1; // xが元の配列に存在しないとき
return UZ[x];
}
};
class UnionFind {
public:
UnionFind() = default;
UnionFind(int N) : par(N), sz(N, 1) {
iota(par.begin(), par.end(), 0);
}
int root(int x) {
if (par[x] == x) return x;
return (par[x] = root(par[x]));
}
bool unite(int x, int y) {
int rx = root(x);
int ry = root(y);
if (rx == ry) return false;
if (sz[rx] < sz[ry]) swap(rx, ry);
sz[rx] += sz[ry];
par[ry] = rx;
return true;
}
bool issame(int x, int y) { return (root(x) == root(y)); }
int size(int x) { return sz[root(x)]; }
vector<vector<int>> groups(int N) {
vector<vector<int>> G(N);
for (int x = 0; x < N; x++) {
G[root(x)].push_back(x);
}
G.erase( remove_if(G.begin(), G.end(),
[&](const vector<int>& V) { return V.empty(); }), G.end());
return G;
}
private:
vector<int> par, sz;
};
template<typename T> struct BIT {
int N; // 要素数
vector<T> bit[2]; // データの格納先
BIT(int N_, int x = 0) {
N = N_ + 1;
bit[0].assign(N, 0); bit[1].assign(N, 0);
if (x != 0) {
for (int i = 0; i < N; i++) add(i, x);
}
}
BIT(const vector<T> &A) {
N = A.size() + 1;
bit[0].assign(N, 0); bit[1].assign(N, 0);
for (int i = 0; i < (int)A.size(); i++) add(i, A[i]);
}
void add_sub(int p, int i, T x) {
while (i < N) { bit[p][i] += x; i += (i & -i); }
}
void add(int l, int r, T x) {
add_sub(0, l + 1, -x * l); add_sub(0, r + 1, x * r);
add_sub(1, l + 1, x); add_sub(1, r + 1, -x);
}
void add(int i, T x) { add(i, i + 1, x); }
T sum_sub(int p, int i) {
T ret = 0;
while (i > 0) { ret += bit[p][i]; i -= (i & -i); }
return ret;
}
T sum(int i) { return sum_sub(0, i) + sum_sub(1, i) * i; }
T sum(int l, int r) { return sum(r) - sum(l); }
T get(int i) { return sum(i, i + 1); }
void set(int i, T x) { T s = get(i); add(i, -s + x); }
};
template<int mod> class Modint {
public:
int val = 0;
Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
Modint(const Modint &r) { val = r.val; }
Modint operator -() { return Modint(-val); } // 単項
Modint operator +(const Modint &r) { return Modint(*this) += r; }
Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
Modint operator -(const Modint &r) { return Modint(*this) -= r; }
Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
Modint operator *(const Modint &r) { return Modint(*this) *= r; }
Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
Modint operator /(const Modint &r) { return Modint(*this) /= r; }
Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置
Modint operator ++(signed) { ++*this; return *this; } // 後置
Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
Modint operator --(signed) { --*this; return *this; }
Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator -=(const int &q) { Modint r(q); if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
Modint &operator /=(const Modint &r) {
int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
Modint &operator /=(const int &q) {
Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
bool operator ==(const Modint& r) { return this -> val == r.val; }
bool operator <(const Modint& r) { return this -> val < r.val; }
bool operator >(const Modint& r) { return this -> val > r.val; }
bool operator !=(const Modint& r) { return this -> val != r.val; }
friend istream &operator >>(istream &is, Modint& x) {
int t; is >> t; x = t; return (is);
}
friend ostream &operator <<(ostream &os, const Modint& x) {
return os << x.val;
}
};
using mint = Modint<MOD>;
mint modpow(const mint &x, int n) {
if (n < 0) return (mint)1 / modpow(x, -n); // 未verify
assert(n >= 0);
if (n == 0) return 1;
mint t = modpow(x, n / 2);
t = t * t;
if (n & 1) t = t * x;
return t;
}
int modpow(__int128_t x, int n, int mod) {
assert(n >= 0 && mod > 0); // TODO: n <= -1
__int128_t ret = 1;
while (n > 0) {
if (n % 2 == 1) ret = ret * x % mod;
x = x * x % mod;
n /= 2;
}
return ret;
}
// int modinv(__int128_t x, int mod) { //
// assert(mod > 0);
// // assert(x > 0);
// if (x == 1 or x == 0) return 1;
// return mod - modinv(mod % x, mod) * (mod / x) % mod;
// }
vector<mint> _fac, _finv, _inv;
void COMinit(int N) {
_fac.resize(N + 1); _finv.resize(N + 1); _inv.resize(N + 1);
_fac[0] = _fac[1] = 1; _finv[0] = _finv[1] = 1; _inv[1] = 1;
for (int i = 2; i <= N; i++) {
_fac[i] = _fac[i-1] * mint(i);
_inv[i] = -_inv[MOD % i] * mint(MOD / i);
_finv[i] = _finv[i - 1] * _inv[i];
}
}
mint FAC(int N) {
if (N < 0) return 0; return _fac[N];
}
mint FACi(int N) {
if (N < 0) return 0; return _finv[N];
}
mint COM(int N, int K) {
if (N < K) return 0; if (N < 0 or K < 0) return 0;
return _fac[N] * _finv[K] * _finv[N - K];
}
mint COMi(int N, int K) {
if (N < K) return 0; if (N < 0 or K < 0) return 0;
return _finv[N] * _fac[K] * _fac[N - K];
}
mint MCOM(const vector<int> &V) {
int N = 0;
for (int i = 0; i < V.size(); i++) N += V[i];
mint ret = _fac[N];
for (int i = 0; i < V.size(); i++) ret *= _finv[V[i]];
return ret;
}
mint PERM(int N, int K) {
if (N < K) return 0; if (N < 0 or K < 0) return 0;
return _fac[N] * _finv[N - K];
}
mint NHK(int N, int K) { // initのサイズに注意
if (N == 0 && K == 0) return 1;
return COM(N + K - 1, K);
}
#pragma endregion
template<typename T, typename C>
struct StaticPointAddRectangleSum {
using BIT = fenwick_tree<C>;
static_assert(is_integral<T>::value, "template parameter T must be integral type");
struct Point {
T x, y;
C w;
};
struct Query {
T l, d, r, u;
};
vector<Point> points;
vector<Query> queries;
StaticPointAddRectangleSum() = default;
StaticPointAddRectangleSum(int n, int q) {
points.reserve(n);
queries.reserve(q);
}
void add_point(T x, T y, C w) {
points.emplace_back(Point{x, y, w});
}
// tatal weight of [l, r) * [d, u) points
void add_query(T l, T d, T r, T u) {
queries.emplace_back(Query{l, d, r, u});
}
vector<C> solve() {
int n = (int) points.size();
int q = (int) queries.size();
vector<C> ans(q);
if (points.empty() or queries.empty()) {
return ans;
}
sort(points.begin(), points.end(), [](const Point &a, const Point &b) {
return a.y < b.y;
});
vector<T> ys;
ys.reserve(n);
for (Point &p : points) {
if (ys.empty() or ys.back() != p.y) ys.emplace_back(p.y);
p.y = (int) ys.size() - 1;
}
ys.shrink_to_fit();
struct Q {
T x;
int d, u;
bool type;
int idx;
};
vector<Q> qs;
qs.reserve(q + q);
for (int i = 0; i < q; i++) {
auto &query = queries[i];
int d = lower_bound(ys.begin(), ys.end(), query.d) - ys.begin();
int u = lower_bound(ys.begin(), ys.end(), query.u) - ys.begin();
qs.emplace_back(Q{query.l, d, u, false, i});
qs.emplace_back(Q{query.r, d, u, true, i});
}
sort(points.begin(), points.end(), [](const Point &a, const Point &b) {
return a.x < b.x;
});
sort(qs.begin(), qs.end(), [](const Q &a, const Q &b) {
return a.x < b.x;
});
int j = 0;
BIT bit(ys.size());
for (auto &query: qs) {
while (j < n and points[j].x < query.x) {
bit.add(points[j].y, points[j].w);
j++;
}
if (query.type) ans[query.idx] += bit.sum(query.d, query.u);
else ans[query.idx] -= bit.sum(query.d, query.u);
}
return ans;
}
};
template<typename T, typename C>
struct DynamicPointAddRectangleSum {
using StaticRectangleSumSolver = StaticPointAddRectangleSum<T, C>;
static_assert(is_integral<T>::value, "template parameter T must be integral type");
struct Point {
T t;
T x, y;
C w;
T l, d, r, u;
};
vector<Point> queries;
DynamicPointAddRectangleSum() = default;
DynamicPointAddRectangleSum(int q) {
queries.reserve(q);
}
void add_point(T x, T y, C w) {
queries.emplace_back(Point{0, x, y, w, 0, 0, 0, 0});
}
// tatal weight of [l, r) * [d, u) points
void add_query(T l, T d, T r, T u) {
queries.emplace_back(Point{1, 0, 0, 0, l, d, r, u});
}
vector<C> solve() {
int q = (int) queries.size();
vector< int > rev(q);
int sz = 0;
for (int i = 0; i < q; i++) {
if (queries[i].t == 1) {
rev[i] = sz++;
}
}
vector<C> ans(sz);
queue<pair<int, int>> range;
range.emplace(0, q);
while (!range.empty()) {
auto[l, r] = range.front();
range.pop();
int m = (l + r) >> 1;
StaticRectangleSumSolver solver;
for (int k = l; k < m; k++) {
if (queries[k].t == 0) {
auto &point = queries[k];
solver.add_point(point.x, point.y, point.w);
}
}
for (int k = m; k < r; k++) {
if (queries[k].t == 1) {
auto &query = queries[k];
solver.add_query(query.l, query.d, query.r, query.u);
}
}
auto sub = solver.solve();
for (int k = m, t = 0; k < r; k++) {
if (queries[k].t == 1) {
ans[rev[k]] += sub[t++];
}
}
if (l + 1 < m) range.emplace(l, m);
if (m + 1 < r) range.emplace(m, r);
}
return ans;
}
};
signed main() {
int N;
cin >> N;
vector<int> X(N), Y(N);
for (int i = 0; i < N; i++) cin >> X[i] >> Y[i];
int P = 0, Q = 0, R = 0, S = 0;
DynamicPointAddRectangleSum<int, int> p(N * 3);
for (int i = 0; i < N; i++) {
p.add_query(X[i] + 1, Y[i] + 1, INF, INF);
p.add_query(-INF, -INF, X[i], Y[i]);
p.add_point(X[i], Y[i], 1);
}
for (auto &&ans : p.solve()) {
P += ans;
}
DynamicPointAddRectangleSum<int, int> q(N * 3);
for (int i = 0; i < N; i++) {
q.add_query(-INF, Y[i] + 1, X[i], INF);
q.add_query(X[i] + 1, -INF, INF, Y[i]);
q.add_point(X[i], Y[i], 1);
}
for (auto &&ans : q.solve()) {
Q += ans;
}
unordered_map<int, int> mpX, mpY;
for (int i = 0; i < N; i++) {
R += i - mpX[X[i]];
S += i - mpY[Y[i]];
mpX[X[i]]++;
mpY[Y[i]]++;
}
cout << (ld)(P - Q) / (ld)(sqrt(R*S)) << endl;
}