結果
| 問題 | No.2338 Range AtCoder Query |
| ユーザー |
 minato
|
| 提出日時 | 2023-06-02 22:39:03 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 724 ms / 4,000 ms |
| コード長 | 20,710 bytes |
| コンパイル時間 | 2,277 ms |
| コンパイル使用メモリ | 169,060 KB |
| 実行使用メモリ | 51,468 KB |
| 最終ジャッジ日時 | 2023-08-28 04:49:25 |
| 合計ジャッジ時間 | 20,734 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge14 |
（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 | 1 ms
4,376 KB |
| testcase_01 | AC | 2 ms
4,376 KB |
| testcase_02 | AC | 2 ms
4,376 KB |
| testcase_03 | AC | 1 ms
4,376 KB |
| testcase_04 | AC | 1 ms
4,376 KB |
| testcase_05 | AC | 1 ms
4,376 KB |
| testcase_06 | AC | 4 ms
4,380 KB |
| testcase_07 | AC | 3 ms
4,376 KB |
| testcase_08 | AC | 3 ms
4,376 KB |
| testcase_09 | AC | 3 ms
4,376 KB |
| testcase_10 | AC | 3 ms
4,384 KB |
| testcase_11 | AC | 608 ms
34,772 KB |
| testcase_12 | AC | 560 ms
33,308 KB |
| testcase_13 | AC | 633 ms
39,352 KB |
| testcase_14 | AC | 591 ms
40,524 KB |
| testcase_15 | AC | 717 ms
41,232 KB |
| testcase_16 | AC | 719 ms
35,420 KB |
| testcase_17 | AC | 724 ms
35,160 KB |
| testcase_18 | AC | 717 ms
35,212 KB |
| testcase_19 | AC | 717 ms
35,300 KB |
| testcase_20 | AC | 716 ms
35,316 KB |
| testcase_21 | AC | 714 ms
35,160 KB |
| testcase_22 | AC | 717 ms
35,204 KB |
| testcase_23 | AC | 712 ms
36,052 KB |
| testcase_24 | AC | 721 ms
35,772 KB |
| testcase_25 | AC | 713 ms
35,256 KB |
| testcase_26 | AC | 294 ms
32,192 KB |
| testcase_27 | AC | 290 ms
32,652 KB |
| testcase_28 | AC | 292 ms
32,212 KB |
| testcase_29 | AC | 572 ms
50,948 KB |
| testcase_30 | AC | 354 ms
13,488 KB |
| testcase_31 | AC | 244 ms
13,496 KB |
| testcase_32 | AC | 444 ms
51,468 KB |
| testcase_33 | AC | 487 ms
35,184 KB |
| testcase_34 | AC | 490 ms
35,212 KB |
ソースコード
#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define all(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
x = 0;
string s;
is >> s;
int n = int(s.size()), it = 0;
if (s[0] == '-') it++;
for (; it < n; it++) x = (x * 10 + s[it] - '0');
if (s[0] == '-') x = -x;
return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
deque<int> deq;
while (x) deq.emplace_front(x % 10), x /= 10;
for (int e : deq) os << e;
return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;}
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define LDB(...) \
long double __VA_ARGS__; \
IN(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define VEC2(type, name1, name2, size) \
vector<type> name1(size), name2(size); \
for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size) \
vector<type> name1(size), name2(size), name3(size); \
for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size) \
vector<type> name1(size), name2(size), name3(size), name4(size); \
for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M) \
vector<vector<type>> name(N, vector<type>(M)); \
IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{"; { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "library-cpp/datastructure/BinaryIndexedTree.hpp"
template <class T> struct BinaryIndexedTree {
int n;
vector<T> data;
BinaryIndexedTree() {
}
BinaryIndexedTree(int n) : n(n), data(n + 1, 0) {
}
int size() const {
return n;
}
/**
* (0-indexed)
* a[i] += x
*/
void add(int i, T x) {
assert(0 <= i and i < n);
for (++i; i <= n; i += i & -i) data[i] += x;
}
// [0,i) (0-indexed) a[0] + … + a[i-1]
T sum(int i) const {
assert(0 <= i and i <= n);
T ret = 0;
for (; i > 0; i -= i & -i) ret += data[i];
return ret;
}
/**
* [l, r) (0-indexed)
* @return a[l] + … + a[r-1]
*/
T sum(int l, int r) const {
if (l >= r) return T(0);
return sum(r) - sum(l);
}
/**
* (0-indexed)
* r = 0 or a[0] + a[1] + ... + a[r-1] < x
* r = n or a[0] + a[1] + ... + a[r] >= x
* a[0] + a[1] + ... + a[r] >= x となる最小の r を返す。
*/
int lower_bound(T x) const {
int k = 1;
int ret = 0;
while ((k << 1) <= n) k <<= 1;
while (k > 0) {
if (ret + k <= n and data[ret + k] < x) {
x -= data[ret + k];
ret += k;
}
k >>= 1;
}
return ret;
}
int upper_bound(T x) const {
return lower_bound(x + 1);
}
#ifdef MINATO_LOCAL
friend ostream& operator<<(ostream& os, const BinaryIndexedTree& r) {
vector<T> v(r.size());
for (int i = 0; i < r.size(); i++) {
v[i] = r.sum(i, i + 1);
}
os << v;
return os;
}
#endif
};
#line 3 "E.cpp"
template <class S, class T> struct PointAddRectangleSum {
using P = pair<S, S>;
int n, log, size, sz;
vector<P> points;
vector<S> xs, ls, rs, ys;
vector<BinaryIndexedTree<T>> BITs;
PointAddRectangleSum() {
}
void push_point(S x, S y) {
points.emplace_back(x, y);
}
void build() {
sort(points.begin(), points.end());
points.erase(unique(points.begin(), points.end()), points.end());
xs.reserve(points.size());
for (const auto& p : points) {
xs.push_back(p.first);
}
xs.erase(unique(xs.begin(), xs.end()), xs.end());
n = int(xs.size());
log = 0;
while ((1 << log) < n) log++;
sz = 1 << log;
BITs.resize(sz * 2);
ls.resize(sz * 2);
rs.resize(sz * 2);
ys.reserve(points.size());
int xs_index = 0;
for (int i = 0; i < int(points.size()); i++) {
if (i > 0 && points[i].first != points[i - 1].first) {
rs[sz + xs_index] = int(ys.size());
xs_index++;
}
if (i == 0 || points[i].first != points[i - 1].first) {
ls[sz + xs_index] = int(ys.size());
}
ys.push_back(points[i].second);
}
rs[sz + n - 1] = int(ys.size());
for (int i = n; i < sz; i++) {
ls[sz + i] = int(ys.size());
rs[sz + i] = int(ys.size());
}
for (int i = 0; i < n; i++) {
BITs[sz + i] = BinaryIndexedTree<T>(rs[sz + i] - ls[sz + i]);
}
for (int i = sz - 1; i >= 1; i--) {
ls[i] = int(ys.size());
vector<int> vs;
vs.reserve(rs[i * 2] - ls[i * 2] + rs[i * 2 + 1] - ls[i * 2 + 1]);
merge(ys.begin() + ls[i * 2], ys.begin() + rs[i * 2],
ys.begin() + ls[i * 2 + 1], ys.begin() + rs[i * 2 + 1],
back_inserter(vs));
vs.erase(unique(vs.begin(), vs.end()), vs.end());
move(vs.begin(), vs.end(), back_inserter(ys));
rs[i] = int(ys.size());
BITs[i] = BinaryIndexedTree<T>(rs[i] - ls[i]);
}
}
void add(S x, S y, T value) {
int k = lower_bound(xs.begin(), xs.end(), x) - xs.begin();
assert(k < n && xs[k] == x);
k += sz;
int l = get_y_index(y, k);
assert(l < rs[k] - ls[k] && ys[ls[k] + l] == y);
BITs[k].add(l, value);
for (int i = 1; i <= log; i++) {
int p = k >> i;
int l = get_y_index(y, p);
assert(l < rs[p] - ls[p] && ys[ls[p] + l] == y);
BITs[p].add(l, value);
}
}
T get(S xl, S xr, S yl, S yr) const {
int l = lower_bound(xs.begin(), xs.end(), xl) - xs.begin();
int r = lower_bound(xs.begin(), xs.end(), xr) - xs.begin();
l += sz;
r += sz;
T ret = 0;
while (l < r) {
if (l & 1) {
int ll = get_y_index(yl, l);
int rr = get_y_index(yr, l);
ret += BITs[l].sum(ll, rr);
l++;
}
if (r & 1) {
r--;
int ll = get_y_index(yl, r);
int rr = get_y_index(yr, r);
ret += BITs[r].sum(ll, rr);
}
l >>= 1;
r >>= 1;
}
return ret;
}
private:
int get_y_index(S y, int x_index) const {
return lower_bound(ys.begin() + ls[x_index], ys.begin() + rs[x_index],
y) -
(ys.begin() + ls[x_index]);
}
};
struct SuccinctIndexableDictionary {
size_t length;
size_t blocks;
vector<unsigned> bit, sum;
SuccinctIndexableDictionary() = default;
SuccinctIndexableDictionary(size_t length)
: length(length), blocks((length + 31) >> 5) {
bit.assign(blocks, 0U);
sum.assign(blocks, 0U);
}
void set(int k) {
bit[k >> 5] |= 1U << (k & 31);
}
void build() {
sum[0] = 0U;
for (int i = 1; i < int(blocks); i++) {
sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
}
}
bool operator[](int k) {
return (bool((bit[k >> 5] >> (k & 31)) & 1));
}
int rank(int k) {
return (sum[k >> 5] +
__builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
}
int rank(bool val, int k) {
return (val ? rank(k) : k - rank(k));
}
};
template <typename T, int MAXLOG> struct WaveletMatrix {
size_t length;
SuccinctIndexableDictionary matrix[MAXLOG];
int mid[MAXLOG];
WaveletMatrix() = default;
WaveletMatrix(vector<T> v) : length(v.size()) {
vector<T> l(length), r(length);
for (int level = MAXLOG - 1; level >= 0; level--) {
matrix[level] = SuccinctIndexableDictionary(length + 1);
int left = 0, right = 0;
for (int i = 0; i < int(length); i++) {
if (((v[i] >> level) & 1)) {
matrix[level].set(i);
r[right++] = v[i];
} else {
l[left++] = v[i];
}
}
mid[level] = left;
matrix[level].build();
v.swap(l);
for (int i = 0; i < right; i++) {
v[left + i] = r[i];
}
}
}
pair<int, int> succ(bool f, int l, int r, int level) {
return {matrix[level].rank(f, l) + mid[level] * f,
matrix[level].rank(f, r) + mid[level] * f};
}
// v[k]
T access(int k) {
T ret = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
bool f = matrix[level][k];
if (f) ret |= T(1) << level;
k = matrix[level].rank(f, k) + mid[level] * f;
}
return ret;
}
T operator[](const int& k) {
return access(k);
}
// count i s.t. (0 <= i < r) && v[i] == x
int rank(const T& x, int r) {
int l = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
tie(l, r) = succ((x >> level) & 1, l, r, level);
}
return r - l;
}
// k-th(0-indexed) smallest number in v[l,r)
T kth_smallest(int l, int r, int k) {
assert(0 <= k && k < r - l);
T ret = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
int cnt =
matrix[level].rank(false, r) - matrix[level].rank(false, l);
bool f = cnt <= k;
if (f) {
ret |= T(1) << level;
k -= cnt;
}
tie(l, r) = succ(f, l, r, level);
}
return ret;
}
// k-th(0-indexed) largest number in v[l,r)
T kth_largest(int l, int r, int k) {
return kth_smallest(l, r, r - l - k - 1);
}
// count i s.t. (l <= i < r) && (v[i] < upper)
int range_freq(int l, int r, T upper) {
int ret = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
bool f = ((upper >> level) & 1);
if (f)
ret +=
matrix[level].rank(false, r) - matrix[level].rank(false, l);
tie(l, r) = succ(f, l, r, level);
}
return ret;
}
// count i s.t. (l <= i < r) && (lower <= v[i] < upper)
int range_freq(int l, int r, T lower, T upper) {
return range_freq(l, r, upper) - range_freq(l, r, lower);
}
// max v[i] s.t. (l <= i < r) && (v[i] < upper)
T prev_value(int l, int r, T upper) {
int cnt = range_freq(l, r, upper);
return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
}
// min v[i] s.t. (l <= i < r) && (lower <= v[i])
T next_value(int l, int r, T lower) {
int cnt = range_freq(l, r, lower);
return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
}
};
void solve() {
INT(N, M, Q);
vec<int> P(N), S(N);
rep(i, N) {
cin >> P[i];
P[i]--;
string s;
cin >> s;
S[i] = s == "AC";
}
VEC2(int, L, R, Q);
L--;
vec<int> nextAC(N, N), preAC(N, -1);
{
vec<int> lastAC(M, -1);
rep(i, N) {
preAC[i] = lastAC[P[i]];
if (S[i]) lastAC[P[i]] = i;
}
}
{
vec<int> lastAC(M, N);
for (int i = N - 1; i >= 0; i--) {
nextAC[i] = lastAC[P[i]];
if (S[i]) lastAC[P[i]] = i;
}
}
vec<pii> ans(Q);
{
vec<int> init(N);
rep(i, N) if (S[i]) init[i] = nextAC[i];
WaveletMatrix<int, 20> wm(init);
rep(i, Q) {
ans[i].first = wm.range_freq(L[i], R[i], R[i], N + 5);
}
}
PointAddRectangleSum<int, int> pas;
rep(i, N) {
if (!S[i]) {
pas.push_point(preAC[i] + 1, nextAC[i]);
pas.push_point(i + 1, nextAC[i]);
}
}
pas.build();
rep(i, N) {
if (!S[i]) {
pas.add(preAC[i] + 1, nextAC[i], 1);
pas.add(i + 1, nextAC[i], -1);
}
}
rep(i, Q) {
ans[i].second = pas.get(0, L[i] + 1, 0, R[i]);
}
for (auto [a, b] : ans) print(a, b);
}
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(20);
cerr << fixed << setprecision(7);
int T = 1;
// cin >> T;
for (int test_case = 1; test_case <= T; test_case++) {
// debug(test_case);
solve();
}
}