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subcrip 2024-05-15 23:16:58 +08:00
parent ca2c65a14d
commit 5588d468ed
Signed by: subcrip
SSH Key Fingerprint: SHA256:dFPFi68d8C87YkFkEBU4TkcrYRySWpekRR1hbnDWUCw
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#pragma GCC optimize("Ofast")
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (requires C++17)
*/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using pid = pair<int, ld>;
using pdi = pair<ld, int>;
using pld = pair<ll, ld>;
using pdl = pair<ld, ll>;
using pdd = pair<ld, ld>;
using tlll = tuple<ll, ll, ll>;
using tlld = tuple<ll, ll, ld>;
using tlli = tuple<ll, ll, int>;
using tldl = tuple<ll, ld, ll>;
using tldd = tuple<ll, ld, ld>;
using tldi = tuple<ll, ld, int>;
using tlil = tuple<ll, int, ll>;
using tlid = tuple<ll, int, ld>;
using tlii = tuple<ll, int, int>;
using tdll = tuple<ld, ll, ll>;
using tdld = tuple<ld, ll, ld>;
using tdli = tuple<ld, ll, int>;
using tddl = tuple<ld, ld, ll>;
using tddd = tuple<ld, ld, ld>;
using tddi = tuple<ld, ld, int>;
using tdil = tuple<ld, int, ll>;
using tdid = tuple<ld, int, ld>;
using tdii = tuple<ld, int, int>;
using till = tuple<int, ll, ll>;
using tild = tuple<int, ll, ld>;
using tili = tuple<int, ll, int>;
using tidl = tuple<int, ld, ll>;
using tidd = tuple<int, ld, ld>;
using tidi = tuple<int, ld, int>;
using tiil = tuple<int, int, ll>;
using tiid = tuple<int, int, ld>;
using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!(var == val)) var = val; else
#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
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);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (auto& x : a) cin >> x;)
#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(string s, string t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(string s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n);
vector<int> ch(n + 1);
vector<vector<int>> hc(n + 1);
for (int i = 1; i <= n; ++i) {
read(int, x);
if (i + x <= n and i + x > 0) {
ch[i] = i + x;
hc[i + x].emplace_back(i);
}
}
vector<int> choice(n + 1, -1);
vector<bool> vis(n + 1);
auto mark = [&] (auto mark, int v) -> int {
if (choice[v] != -1) return choice[v];
if (ch[v] == 0) {
choice[v] = 1;
} else if (vis[ch[v]]) {
choice[v] = 0;
} else {
vis[v] = 1;
choice[v] = mark(mark, ch[v]);
vis[v] = 0;
}
return choice[v];
};
for (int i = 1; i <= n; ++i) {
if (choice[i] == -1) {
mark(mark, i);
}
}
int choices = count(choice.begin(), choice.end(), 1);
vis.assign(n + 1, 0);
auto dfs2 = [&] (auto dfs2, int v) -> void {
if (not choice[v]) return;
choice[v] = 0, --choices;
for (auto&& u : hc[v]) {
dfs2(dfs2, u);
}
};
ll res = 0;
int cnt = 0;
// debug(choice);
auto dfs = [&] (auto dfs, int v) -> int {
if (vis[v]) return false;
if (v == 0) return true;
dfs2(dfs2, v);
// debug(make_tuple(v, choices));
res += n + 1 + choices;
vis[v] = 1;
cnt += 1;
return dfs(dfs, ch[v]);
};
if (dfs(dfs, 1)) {
res += ll(1) * (n - cnt) * (2 * n + 1);
}
cout << res << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#pragma GCC optimize("Ofast")
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (requires C++17)
*/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using pid = pair<int, ld>;
using pdi = pair<ld, int>;
using pld = pair<ll, ld>;
using pdl = pair<ld, ll>;
using pdd = pair<ld, ld>;
using tlll = tuple<ll, ll, ll>;
using tlld = tuple<ll, ll, ld>;
using tlli = tuple<ll, ll, int>;
using tldl = tuple<ll, ld, ll>;
using tldd = tuple<ll, ld, ld>;
using tldi = tuple<ll, ld, int>;
using tlil = tuple<ll, int, ll>;
using tlid = tuple<ll, int, ld>;
using tlii = tuple<ll, int, int>;
using tdll = tuple<ld, ll, ll>;
using tdld = tuple<ld, ll, ld>;
using tdli = tuple<ld, ll, int>;
using tddl = tuple<ld, ld, ll>;
using tddd = tuple<ld, ld, ld>;
using tddi = tuple<ld, ld, int>;
using tdil = tuple<ld, int, ll>;
using tdid = tuple<ld, int, ld>;
using tdii = tuple<ld, int, int>;
using till = tuple<int, ll, ll>;
using tild = tuple<int, ll, ld>;
using tili = tuple<int, ll, int>;
using tidl = tuple<int, ld, ll>;
using tidd = tuple<int, ld, ld>;
using tidi = tuple<int, ld, int>;
using tiil = tuple<int, int, ll>;
using tiid = tuple<int, int, ld>;
using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!(var == val)) var = val; else
#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
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);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (auto& x : a) cin >> x;)
#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(string s, string t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(string s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n, m);
vector<vector<int>> a(n, vector<int>(m + 1));
for (int i = 0; i < n; ++i) {
for (int j = 1; j <= m; ++j) {
cin >> a[i][j];
}
}
vector<int> res(n);
auto rev = [&] (const vector<int>& x) {
vector<int> res(m + 1);
for (int i = 0; i <= m; ++i) {
int curr = x[i];
res[curr] = i;
}
return res;
};
vector<array<int, 11>> trie(1);
auto insert = [&] (const vector<int>& x) -> void {
int curr = 0;
for (int i = 1; i <= m; ++i) {
// debug(i), debug(x[i]);
// debug(curr);
if (not trie[curr][x[i]]) {
trie[curr][x[i]] = trie.size();
trie.push_back({});
}
curr = trie[curr][x[i]];
}
};
auto query = [&] (const vector<int>& x) -> int {
int curr = 0;
for (int i = 1; i <= m; ++i) {
if (not trie[curr][x[i]]) {
return i - 1;
}
curr = trie[curr][x[i]];
}
return m;
};
for (int i = 0; i < n; ++i) {
insert(rev(a[i]));
}
for (int i = 0; i < n; ++i) {
cout << query(a[i]) << " \n"[i + 1 == n];
}
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#pragma GCC optimize("Ofast")
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (requires C++17)
*/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using pid = pair<int, ld>;
using pdi = pair<ld, int>;
using pld = pair<ll, ld>;
using pdl = pair<ld, ll>;
using pdd = pair<ld, ld>;
using tlll = tuple<ll, ll, ll>;
using tlld = tuple<ll, ll, ld>;
using tlli = tuple<ll, ll, int>;
using tldl = tuple<ll, ld, ll>;
using tldd = tuple<ll, ld, ld>;
using tldi = tuple<ll, ld, int>;
using tlil = tuple<ll, int, ll>;
using tlid = tuple<ll, int, ld>;
using tlii = tuple<ll, int, int>;
using tdll = tuple<ld, ll, ll>;
using tdld = tuple<ld, ll, ld>;
using tdli = tuple<ld, ll, int>;
using tddl = tuple<ld, ld, ll>;
using tddd = tuple<ld, ld, ld>;
using tddi = tuple<ld, ld, int>;
using tdil = tuple<ld, int, ll>;
using tdid = tuple<ld, int, ld>;
using tdii = tuple<ld, int, int>;
using till = tuple<int, ll, ll>;
using tild = tuple<int, ll, ld>;
using tili = tuple<int, ll, int>;
using tidl = tuple<int, ld, ll>;
using tidd = tuple<int, ld, ld>;
using tidi = tuple<int, ld, int>;
using tiil = tuple<int, int, ll>;
using tiid = tuple<int, int, ld>;
using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!(var == val)) var = val; else
#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
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);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (auto& x : a) cin >> x;)
#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(string s, string t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(string s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n);
readvec(pll, a, n);
sort(a.begin(), a.end());
ll res = INFLL;
ll max_b = -INFLL;
set<pli> b;
for (int i = 0; i < n; ++i) b.emplace(a[i].second, i);
for (int i = n - 1; ~i; --i) {
auto [x, y] = a[i];
res = min(res, abs(x - max_b));
b.erase({y, i});
auto it = b.lower_bound({x, 0});
if (it != b.end()) {
res = min(res, abs(x - max(max_b, it->first)));
}
if (it != b.begin()) {
res = min(res, abs(x - max(max_b, (--it)->first)));
}
max_b = max(max_b, y);
}
cout << res << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#pragma GCC optimize("Ofast")
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (requires C++17)
*/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using pid = pair<int, ld>;
using pdi = pair<ld, int>;
using pld = pair<ll, ld>;
using pdl = pair<ld, ll>;
using pdd = pair<ld, ld>;
using tlll = tuple<ll, ll, ll>;
using tlld = tuple<ll, ll, ld>;
using tlli = tuple<ll, ll, int>;
using tldl = tuple<ll, ld, ll>;
using tldd = tuple<ll, ld, ld>;
using tldi = tuple<ll, ld, int>;
using tlil = tuple<ll, int, ll>;
using tlid = tuple<ll, int, ld>;
using tlii = tuple<ll, int, int>;
using tdll = tuple<ld, ll, ll>;
using tdld = tuple<ld, ll, ld>;
using tdli = tuple<ld, ll, int>;
using tddl = tuple<ld, ld, ll>;
using tddd = tuple<ld, ld, ld>;
using tddi = tuple<ld, ld, int>;
using tdil = tuple<ld, int, ll>;
using tdid = tuple<ld, int, ld>;
using tdii = tuple<ld, int, int>;
using till = tuple<int, ll, ll>;
using tild = tuple<int, ll, ld>;
using tili = tuple<int, ll, int>;
using tidl = tuple<int, ld, ll>;
using tidd = tuple<int, ld, ld>;
using tidi = tuple<int, ld, int>;
using tiil = tuple<int, int, ll>;
using tiid = tuple<int, int, ld>;
using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!(var == val)) var = val; else
#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
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);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); copy_n(ii<type>(cin), (n), a.begin());)
#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(string s, string t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(string s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
/////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n);
adj(ch, n);
for (int i = 0; i < n - 1; ++i) {
read(int, u, v);
edge(ch, u, v);
}
vector<int> max_dist(n + 1), max_depth(n + 1);
auto get = [&] (auto get, int v, int pa) -> int {
int curr = 0;
for (auto&& u : ch[v]) {
if (u == pa) continue;
curr = max(curr, get(get, u, v) + 1);
}
max_depth[v] = curr;
return curr;
};
get(get, 1, 0);
// debug(max_depth);
auto dfs = [&] (auto dfs, int v, int pa, int up) -> void {
// debug(make_tuple(v, up));
max_dist[v] = max(max_depth[v], up);
int max_depth1 = -1, max_depth_u1 = -1;
int max_depth2 = -1, max_depth_u2 = -1;
for (auto&& u : ch[v]) {
if (u == pa) continue;
int curr_depth = max_depth[u];
// debug(make_tuple(u, curr_depth));
if (curr_depth > max_depth1) {
max_depth2 = max_depth1, max_depth_u2 = max_depth_u1;
max_depth1 = curr_depth, max_depth_u1 = u;
} else if (curr_depth > max_depth2) {
max_depth2 = curr_depth, max_depth_u2 = u;
}
}
// debug(make_tuple(max_depth1, max_depth2));
for (auto&& u : ch[v]) {
if (u == pa) continue;
if (u == max_depth_u1) {
dfs(dfs, u, v, max(up, max_depth2 + 1) + 1);
} else {
dfs(dfs, u, v, max(up, max_depth1 + 1) + 1);
}
}
};
dfs(dfs, 1, 0, 0);
// debug(max_dist);
vector<int> diff(n + 2);
for (int i = 1; i <= n; ++i) {
diff[max_dist[i] + 1] += 1;
}
vector<int> res;
int curr = 0;
for (int i = 1; i <= n; ++i) {
curr += diff[i];
if (curr < n) {
res.emplace_back(1 + curr);
} else {
res.emplace_back(curr);
}
}
putvec(res);
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#pragma GCC optimize("Ofast")
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (requires C++17)
*/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using pid = pair<int, ld>;
using pdi = pair<ld, int>;
using pld = pair<ll, ld>;
using pdl = pair<ld, ll>;
using pdd = pair<ld, ld>;
using tlll = tuple<ll, ll, ll>;
using tlld = tuple<ll, ll, ld>;
using tlli = tuple<ll, ll, int>;
using tldl = tuple<ll, ld, ll>;
using tldd = tuple<ll, ld, ld>;
using tldi = tuple<ll, ld, int>;
using tlil = tuple<ll, int, ll>;
using tlid = tuple<ll, int, ld>;
using tlii = tuple<ll, int, int>;
using tdll = tuple<ld, ll, ll>;
using tdld = tuple<ld, ll, ld>;
using tdli = tuple<ld, ll, int>;
using tddl = tuple<ld, ld, ll>;
using tddd = tuple<ld, ld, ld>;
using tddi = tuple<ld, ld, int>;
using tdil = tuple<ld, int, ll>;
using tdid = tuple<ld, int, ld>;
using tdii = tuple<ld, int, int>;
using till = tuple<int, ll, ll>;
using tild = tuple<int, ll, ld>;
using tili = tuple<int, ll, int>;
using tidl = tuple<int, ld, ll>;
using tidd = tuple<int, ld, ld>;
using tidi = tuple<int, ld, int>;
using tiil = tuple<int, int, ll>;
using tiid = tuple<int, int, ld>;
using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!(var == val)) var = val; else
#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
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);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); copy_n(ii<type>(cin), (n), a.begin());)
#define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(string s, string t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(string s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
#define DUMP_TEST_CASE 1393
#define TOT_TEST_CASE 10000
void dump() {
read(int, n);
read(ll, k);
readvec(ll, left_vec, n);
readvec(ll, right_vec, n);
cout << n << ' ' << k << endl;
putvec(left_vec);
putvec(right_vec);
}
void dump_ignore() {
read(int, n);
read(ll, k);
readvec(ll, left_vec, n);
readvec(ll, right_vec, n);
}
void prep() {}
void solve() {
read(int, n);
read(ll, k);
readvec(ll, left_vec, n);
readvec(ll, right_vec, n);
vector<pll> a = zip<ll, ll>(left_vec.begin(), left_vec.end(), right_vec.begin(), right_vec.end());
ll left = 0, right = -1;
vector<ll> length, lf, rf;
for (auto&& [l, r] : a) {
if (l > right + 1) {
if (right - left + 1 != 0) length.emplace_back(right - left + 1);
lf.emplace_back(l);
rf.emplace_back(r);
left = l;
right = r;
} else {
right = r;
}
}
length.emplace_back(right - left + 1);
int m = length.size();
ll res = INFLL;
int r = 0;
ll curr = 0;
ll cnt1 = 0;
for (int i = 0; i < m; ++i) {
while (r < m and curr < k) {
curr += length[r];
if (length[r] == 1) cnt1 += 1;
++r;
}
if (curr < k) break;
ll use = max(ll(0), min(curr - k, cnt1));
res = min(res, rf[r - 1] - (curr - k) + use + (r - i - use) * 2);
curr -= length[i];
if (length[i] == 1) cnt1 -= 1;
}
cout << (res == INFLL ? -1 : res) << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

128
src/bin/ctext_out.cc
View File

@ -15,7 +15,7 @@ using namespace std;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a; #define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {} constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __() #define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) decltype(container)::value_type #define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */ /* type aliases */
#if LONG_LONG_MAX != INT64_MAX #if LONG_LONG_MAX != INT64_MAX
@ -68,6 +68,7 @@ using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>; template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>; template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>; template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */ /* constants */
constexpr int INF = 0x3f3f3f3f; constexpr int INF = 0x3f3f3f3f;
@ -202,10 +203,17 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
template<typename T> void __read(T& x) { cin >> x; } template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); } template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);) #define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];) #define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (auto& x : a) cin >> x;)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;) #define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;) #define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;) #define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) { template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}"; out << "{" << p.first << ", " << p.second << "}";
return out; return out;
@ -391,10 +399,46 @@ template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, Ran
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) { template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); }); std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
} }
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
///////////////////////////////////////////////////////// /////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE // #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219 // #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {} void dump() {}
@ -403,43 +447,51 @@ void dump_ignore() {}
void prep() {} void prep() {}
void solve() { void solve() {
read(int, n); read(int, n, m);
readvec(int, a, n); vector<vector<int>> a(n, vector<int>(m + 1));
int sq = sqrt(n); for (int i = 0; i < n; ++i) {
read(int, q); for (int j = 1; j <= m; ++j) {
vector<ll> res(q); cin >> a[i][j];
vector<vector<pii>> req(n + 1);
for (int t = 0; t < q; ++t) {
read(int, i, s);
--i;
if (s < sq) {
req[s].emplace_back(i, t);
} else {
ll curr = 0;
for (int j = i; j < n; j += s) {
curr += a[j];
}
res[t] = curr;
} }
} }
vector<ll> ss(n); vector<int> res(n);
for (int s = 1; s < sq; ++s) { auto rev = [&] (const vector<int>& x) {
sort(req[s].begin(), req[s].end(), greater()); vector<int> res(m + 1);
int ptr = 0; for (int i = 0; i <= m; ++i) {
ss.assign(n, 0); int curr = x[i];
for (int i = n - 1; ~i; --i) { res[curr] = i;
if (i + s >= n) {
ss[i] = a[i];
} else {
ss[i] = a[i] + ss[i + s];
}
while (ptr < req[s].size() and req[s][ptr].first == i) {
res[req[s][ptr].second] = ss[i];
++ptr;
}
} }
return res;
};
vector<array<int, 11>> trie(1);
auto insert = [&] (const vector<int>& x) -> void {
int curr = 0;
for (int i = 1; i <= m; ++i) {
// debug(i), debug(x[i]);
// debug(curr);
if (not trie[curr][x[i]]) {
trie[curr][x[i]] = trie.size();
trie.push_back({});
}
curr = trie[curr][x[i]];
}
};
auto query = [&] (const vector<int>& x) -> int {
int curr = 0;
for (int i = 1; i <= m; ++i) {
if (not trie[curr][x[i]]) {
return i - 1;
}
curr = trie[curr][x[i]];
}
return m;
};
for (int i = 0; i < n; ++i) {
insert(rev(a[i]));
}
for (int i = 0; i < n; ++i) {
cout << query(a[i]) << " \n"[i + 1 == n];
} }
copy(res.begin(), res.end(), oi<ll>(cout, "\n"));
} }
int main() { int main() {
@ -454,7 +506,7 @@ int main() {
read(int, t); read(int, t);
for (int i = 0; i < t; ++i) { for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE #ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) { if (t < (TOT_TEST_CASE)) {
solve(); solve();
} else if (i + 1 == (DUMP_TEST_CASE)) { } else if (i + 1 == (DUMP_TEST_CASE)) {
dump(); dump();

19
src/bin/std.in
View File

@ -1,7 +1,18 @@
4
2 3 5 7
3 3
1 3 3 4
2 3 2 4 1 3
1 2 4 3
2 1 3 4
2 2 2 2
1 2
2 1
8 10
3 4 9 6 10 2 7 8 1 5
3 9 1 8 5 7 4 10 2 6
3 10 1 7 5 9 6 4 2 8
1 2 3 4 8 6 10 7 9 5
1 2 3 4 10 6 8 5 7 9
9 6 1 2 10 4 7 8 3 5
7 9 3 2 5 6 4 8 1 10
9 4 3 7 5 6 1 10 8 2

1
src/bin/std.out
View File

@ -0,0 +1 @@
1 1 3 5 5

52
src/bin/template.cc
View File

@ -15,7 +15,7 @@ using namespace std;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a; #define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {} constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __() #define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) decltype(container)::value_type #define __as_typeof(container) remove_reference<decltype(container)>::type
/* type aliases */ /* type aliases */
#if LONG_LONG_MAX != INT64_MAX #if LONG_LONG_MAX != INT64_MAX
@ -68,6 +68,7 @@ using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>; template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>; template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>; template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */ /* constants */
constexpr int INF = 0x3f3f3f3f; constexpr int INF = 0x3f3f3f3f;
@ -202,10 +203,17 @@ template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, s
template<typename T> void __read(T& x) { cin >> x; } template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); } template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);) #define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];) #define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (auto& x : a) cin >> x;)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;) #define readvec1(type, a, n) __AS_PROCEDURE(vector<type> a((n) + 1); copy_n(ii<type>(cin), (n), a.begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy(a.begin(), a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy(a.begin() + 1, a.end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;) #define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;) #define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) { template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}"; out << "{" << p.first << ", " << p.second << "}";
return out; return out;
@ -391,10 +399,46 @@ template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, Ran
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) { template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); }); std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
} }
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; a_it != a_last and b_it != b_last; ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
///////////////////////////////////////////////////////// /////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219 // #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {} void dump() {}
@ -417,7 +461,7 @@ int main() {
read(int, t); read(int, t);
for (int i = 0; i < t; ++i) { for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE #ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) { if (t < (TOT_TEST_CASE)) {
solve(); solve();
} else if (i + 1 == (DUMP_TEST_CASE)) { } else if (i + 1 == (DUMP_TEST_CASE)) {
dump(); dump();

482
src/bin/test.cc
View File

@ -1,474 +1,16 @@
#pragma GCC optimize("Ofast") #include <bits/stdc++.h>
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (requires C++17)
*/
#include<bits/stdc++.h>
using namespace std; using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) decltype(container)::value_type
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using pid = pair<int, ld>;
using pdi = pair<ld, int>;
using pld = pair<ll, ld>;
using pdl = pair<ld, ll>;
using pdd = pair<ld, ld>;
using tlll = tuple<ll, ll, ll>;
using tlld = tuple<ll, ll, ld>;
using tlli = tuple<ll, ll, int>;
using tldl = tuple<ll, ld, ll>;
using tldd = tuple<ll, ld, ld>;
using tldi = tuple<ll, ld, int>;
using tlil = tuple<ll, int, ll>;
using tlid = tuple<ll, int, ld>;
using tlii = tuple<ll, int, int>;
using tdll = tuple<ld, ll, ll>;
using tdld = tuple<ld, ll, ld>;
using tdli = tuple<ld, ll, int>;
using tddl = tuple<ld, ld, ll>;
using tddd = tuple<ld, ld, ld>;
using tddi = tuple<ld, ld, int>;
using tdil = tuple<ld, int, ll>;
using tdid = tuple<ld, int, ld>;
using tdii = tuple<ld, int, int>;
using till = tuple<int, ll, ll>;
using tild = tuple<int, ll, ld>;
using tili = tuple<int, ll, int>;
using tidl = tuple<int, ld, ll>;
using tidd = tuple<int, ld, ld>;
using tidi = tuple<int, ld, int>;
using tiil = tuple<int, int, ll>;
using tiid = tuple<int, int, ld>;
using tiii = tuple<int, int, int>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!(var == val)) var = val; else
#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;)
#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
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);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w), ch[v].emplace_back(u, w);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, w) __AS_PROCEDURE(ch[u].emplace_back(v, w);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(string s, string t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(string s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
void operator+=(const MLL& rhs) { val = (*this + rhs).val; }
void operator-=(const MLL& rhs) { val = (*this - rhs).val; }
void operator*=(const MLL& rhs) { val = (*this * rhs).val; }
void operator/=(const MLL& rhs) { val = (*this / rhs).val; }
void operator%=(const MLL& rhs) { val = (*this % rhs).val; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
/////////////////////////////////////////////////////////
vector<vector<vector<pair<int, pair<ll,vector<int>>>>>> dp(1 << 14, vector<vector<pair<int, pair<ll, vector<int>>>>>(14, vector<pair<int, pair<ll, vector<int>>>>(14, {INF, {}})));
class Solution {
public:
vector<int> findPermutation(vector<int>& nums) {
int n = nums.size();
for (int i = 0; i < (1 << n); ++i) {
for (int j = 0; j < n; ++j) {
for (int k = 0; k < n; ++k) {
dp[i][j][k].first = INF;
dp[i][j][k].second.first = 0;
dp[i][j][k].second.second.clear();
}
}
}
vector<pii> a;
for (int i = 0; i < n; ++i) {
a.emplace_back(nums[i], i);
}
for (int i = 0; i < n; ++i) {
dp[1 << i][a[i].first][a[i].second] = {abs(a[i].first - a[i].second), {a[i].second, {a[i].second}}};
}
for (int i = 2; i <= n; ++i) {
for (int mask = 0; mask < (1 << n); ++mask) {
if (popcount(mask) != i) continue;
for (int b = 0; b < n; ++b) {
if (((mask >> b) & 1) == 0) {
continue;
}
// use b
int prev_mask = mask ^ (1 << b);
for (int j = 0; j < n; ++j) {
int use = 0; int cost = dp[mask][j][a[b].second].first;
for (int k = 0; k < n; ++k) {
int delta = -abs(j - k) + abs(k - a[b].first) + abs(j - a[b].second);
if (dp[prev_mask][j][k].first + delta < cost or dp[prev_mask][j][k].first + delta == cost and dp[prev_mask][j][k].second.first < dp[prev_mask][j][use].second.first) {
cost = dp[prev_mask][j][k].first + delta;
use = k;
}
}
if (cost != INF) {
vector<int> new_vec = dp[prev_mask][j][use].second.second;
ll new_hash = dp[prev_mask][j][use].second.first;
new_vec.emplace_back(a[b].second);
new_hash = new_hash * 14 + a[b].second;
if (cost < dp[mask][j][a[b].second].first or cost == dp[mask][j][a[b].second].first and new_hash < dp[mask][j][a[b].second].second.first) {
dp[mask][j][a[b].second].second.second = new_vec;
dp[mask][j][a[b].second].second.first = new_hash;
dp[mask][j][a[b].second].first = cost;
}
}
}
}
}
}
int cost = INF;
ll hs = INFLL;
vector<int> res;
for (int j = 0; j < n; ++j) {
for (int k = 0; k < n; ++k) {
if (dp[(1 << n) - 1][j][k].first < INF and (dp[(1 << n) - 1][j][k].first < cost or dp[(1 << n) - 1][j][k].first == cost and dp[(1 << n) - 1][j][k].second.first < hs)) {
res = dp[(1 << n) - 1][j][k].second.second;
hs = dp[(1 << n) - 1][j][k].second.first;
// putvec(res);
cost = dp[(1 << n) - 1][j][k].first;
}
}
}
// cout << cost << endl;
return res;
}
};
int main() { int main() {
read(int, n); int m = 4;
readvec(int, a, n); auto rev = [&] (const vector<int>& x) {
cout << Solution().findPermutation(a) << endl; vector<int> res(m + 1);
for (int i = 0; i < m; ++i) {
int curr = x[i];
res[curr] = i + 1;
}
return res;
};
auto res = rev({2, 1, 3, 4});
for (auto&& x : res)cout << x << endl;
} }

26
src/bin/test.py
View File

@ -1,5 +1,21 @@
n = 300000 from random import randint
print(n) from os import system
print('1 ' * n)
print(n) while 1:
print(f'1 {n}\n' * n) n = 5
ipt = str(n) + '\n'
for i in range(2, n + 1):
ipt += f'{randint(1, i - 1)} {i}\n'
with open('std.in', 'w') as f:
f.write(ipt)
system('./bad < std.in > std.out')
with open('std.out') as f:
bad = f.read().strip()
system('./good < std.in > std.out')
with open('std.out') as f:
good = f.read().strip()
if bad != good:
print('input:', ipt)
print('bad:', bad)
print('good:', good)
break