結果
| 問題 | No.1773 Love Triangle |
| ユーザー |
 yosupot
|
| 提出日時 | 2021-12-04 02:15:28 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 91 ms / 2,000 ms |
| コード長 | 41,194 bytes |
| コンパイル時間 | 1,665 ms |
| コンパイル使用メモリ | 143,412 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-06 07:13:37 |
| 合計ジャッジ時間 | 8,552 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 33 ms
6,812 KB |
| testcase_01 | AC | 34 ms
6,940 KB |
| testcase_02 | AC | 34 ms
6,944 KB |
| testcase_03 | AC | 34 ms
6,940 KB |
| testcase_04 | AC | 36 ms
6,944 KB |
| testcase_05 | AC | 34 ms
6,944 KB |
| testcase_06 | AC | 35 ms
6,940 KB |
| testcase_07 | AC | 36 ms
6,940 KB |
| testcase_08 | AC | 34 ms
6,940 KB |
| testcase_09 | AC | 35 ms
6,940 KB |
| testcase_10 | AC | 34 ms
6,940 KB |
| testcase_11 | AC | 34 ms
6,940 KB |
| testcase_12 | AC | 35 ms
6,944 KB |
| testcase_13 | AC | 34 ms
6,944 KB |
| testcase_14 | AC | 34 ms
6,944 KB |
| testcase_15 | AC | 35 ms
6,940 KB |
| testcase_16 | AC | 34 ms
6,940 KB |
| testcase_17 | AC | 34 ms
6,944 KB |
| testcase_18 | AC | 59 ms
6,944 KB |
| testcase_19 | AC | 36 ms
6,944 KB |
| testcase_20 | AC | 38 ms
6,940 KB |
| testcase_21 | AC | 35 ms
6,940 KB |
| testcase_22 | AC | 38 ms
6,944 KB |
| testcase_23 | AC | 35 ms
6,940 KB |
| testcase_24 | AC | 36 ms
6,940 KB |
| testcase_25 | AC | 38 ms
6,940 KB |
| testcase_26 | AC | 35 ms
6,940 KB |
| testcase_27 | AC | 35 ms
6,944 KB |
| testcase_28 | AC | 35 ms
6,940 KB |
| testcase_29 | AC | 36 ms
6,940 KB |
| testcase_30 | AC | 52 ms
6,944 KB |
| testcase_31 | AC | 37 ms
6,940 KB |
| testcase_32 | AC | 36 ms
6,940 KB |
| testcase_33 | AC | 38 ms
6,944 KB |
| testcase_34 | AC | 36 ms
6,944 KB |
| testcase_35 | AC | 36 ms
6,944 KB |
| testcase_36 | AC | 44 ms
6,944 KB |
| testcase_37 | AC | 34 ms
6,944 KB |
| testcase_38 | AC | 80 ms
6,940 KB |
| testcase_39 | AC | 78 ms
6,944 KB |
| testcase_40 | AC | 81 ms
6,944 KB |
| testcase_41 | AC | 85 ms
6,940 KB |
| testcase_42 | AC | 87 ms
6,944 KB |
| testcase_43 | AC | 91 ms
6,944 KB |
| testcase_44 | AC | 86 ms
6,940 KB |
| testcase_45 | AC | 80 ms
6,944 KB |
| testcase_46 | AC | 84 ms
6,940 KB |
| testcase_47 | AC | 87 ms
6,940 KB |
| testcase_48 | AC | 81 ms
6,940 KB |
| testcase_49 | AC | 80 ms
6,940 KB |
| testcase_50 | AC | 81 ms
6,944 KB |
| testcase_51 | AC | 87 ms
6,944 KB |
| testcase_52 | AC | 82 ms
6,940 KB |
| testcase_53 | AC | 81 ms
6,944 KB |
| testcase_54 | AC | 85 ms
6,944 KB |
| testcase_55 | AC | 88 ms
6,940 KB |
| testcase_56 | AC | 80 ms
6,940 KB |
| testcase_57 | AC | 82 ms
6,940 KB |
| testcase_58 | AC | 80 ms
6,944 KB |
| testcase_59 | AC | 80 ms
6,940 KB |
| testcase_60 | AC | 80 ms
6,940 KB |
| testcase_61 | AC | 78 ms
6,940 KB |
| testcase_62 | AC | 80 ms
6,940 KB |
| testcase_63 | AC | 78 ms
6,944 KB |
| testcase_64 | AC | 83 ms
6,940 KB |
| testcase_65 | AC | 81 ms
6,940 KB |
| testcase_66 | AC | 85 ms
6,940 KB |
| testcase_67 | AC | 82 ms
6,940 KB |
| testcase_68 | AC | 83 ms
6,944 KB |
| testcase_69 | AC | 81 ms
6,940 KB |
| testcase_70 | AC | 86 ms
6,944 KB |
| testcase_71 | AC | 84 ms
6,940 KB |
| testcase_72 | AC | 82 ms
6,940 KB |
| testcase_73 | AC | 81 ms
6,940 KB |
| testcase_74 | AC | 88 ms
6,940 KB |
| testcase_75 | AC | 84 ms
6,940 KB |
| testcase_76 | AC | 77 ms
6,940 KB |
| testcase_77 | AC | 79 ms
6,940 KB |
| testcase_78 | AC | 34 ms
6,944 KB |
| testcase_79 | AC | 36 ms
6,944 KB |
| testcase_80 | AC | 37 ms
6,944 KB |
| testcase_81 | AC | 59 ms
6,940 KB |
| testcase_82 | AC | 54 ms
6,940 KB |
| testcase_83 | AC | 41 ms
6,940 KB |
| testcase_84 | AC | 42 ms
6,944 KB |
| testcase_85 | AC | 42 ms
6,940 KB |
| testcase_86 | AC | 37 ms
6,944 KB |
| testcase_87 | AC | 38 ms
6,944 KB |
| testcase_88 | AC | 36 ms
6,940 KB |
| testcase_89 | AC | 38 ms
6,940 KB |
| testcase_90 | AC | 48 ms
6,940 KB |
| testcase_91 | AC | 51 ms
6,940 KB |
| testcase_92 | AC | 40 ms
6,940 KB |
ソースコード
//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL
#include <unistd.h>
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>
namespace yosupo {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
} // namespace internal
int bsf(unsigned int n) { return __builtin_ctz(n); }
int bsf(unsigned long n) { return __builtin_ctzl(n); }
int bsf(unsigned long long n) { return __builtin_ctzll(n); }
int bsf(unsigned __int128 n) {
unsigned long long low = (unsigned long long)(n);
unsigned long long high = (unsigned long long)(n >> 64);
return low ? __builtin_ctzll(low) : 64 + __builtin_ctzll(high);
}
int bsr(unsigned int n) {
return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n);
}
int bsr(unsigned long n) {
return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n);
}
int bsr(unsigned long long n) {
return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n);
}
int bsr(unsigned __int128 n) {
unsigned long long low = (unsigned long long)(n);
unsigned long long high = (unsigned long long)(n >> 64);
return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low);
}
int popcnt(unsigned int n) { return __builtin_popcount(n); }
int popcnt(unsigned long n) { return __builtin_popcountl(n); }
int popcnt(unsigned long long n) { return __builtin_popcountll(n); }
} // namespace yosupo
#include <cassert>
#include <numeric>
#include <type_traits>
namespace yosupo {
namespace internal {
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value ||
internal::is_signed_int128<T>::value ||
internal::is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace yosupo
namespace yosupo {
struct Scanner {
public:
Scanner(const Scanner&) = delete;
Scanner& operator=(const Scanner&) = delete;
Scanner(FILE* fp) : fd(fileno(fp)) { line[0] = 127; }
void read() {}
template <class H, class... T> void read(H& h, T&... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
int read_unsafe() { return 0; }
template <class H, class... T> int read_unsafe(H& h, T&... t) {
bool f = read_single(h);
if (!f) return 0;
return 1 + read_unsafe(t...);
}
int close() { return ::close(fd); }
private:
static constexpr int SIZE = 1 << 15;
int fd = -1;
std::array<char, SIZE + 1> line;
int st = 0, ed = 0;
bool eof = false;
bool read_single(std::string& ref) {
if (!skip_space()) return false;
ref = "";
while (true) {
char c = top();
if (c <= ' ') break;
ref += c;
st++;
}
return true;
}
bool read_single(double& ref) {
std::string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
template <class T,
std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
bool read_single(T& ref) {
if (!skip_space<50>()) return false;
ref = top();
st++;
return true;
}
template <class T,
internal::is_signed_int_t<T>* = nullptr,
std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
bool read_single(T& sref) {
using U = internal::to_unsigned_t<T>;
if (!skip_space<50>()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
U ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
sref = neg ? -ref : ref;
return true;
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
bool read_single(U& ref) {
if (!skip_space<50>()) return false;
ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
return true;
}
bool reread() {
if (ed - st >= 50) return true;
if (st > SIZE / 2) {
std::memmove(line.data(), line.data() + st, ed - st);
ed -= st;
st = 0;
}
if (eof) return false;
auto u = ::read(fd, line.data() + ed, SIZE - ed);
if (u == 0) {
eof = true;
line[ed] = '\0';
u = 1;
}
ed += int(u);
line[ed] = char(127);
return true;
}
char top() {
if (st == ed) {
bool f = reread();
assert(f);
}
return line[st];
}
template <int TOKEN_LEN = 0> bool skip_space() {
while (true) {
while (line[st] <= ' ') st++;
if (ed - st > TOKEN_LEN) return true;
if (st > ed) st = ed;
for (auto i = st; i < ed; i++) {
if (line[i] <= ' ') return true;
}
if (!reread()) return false;
}
}
};
struct Printer {
public:
template <char sep = ' ', bool F = false> void write() {}
template <char sep = ' ', bool F = false, class H, class... T>
void write(const H& h, const T&... t) {
if (F) write_single(sep);
write_single(h);
write<true>(t...);
}
template <char sep = ' ', class... T> void writeln(const T&... t) {
write<sep>(t...);
write_single('\n');
}
Printer(FILE* _fp) : fd(fileno(_fp)) {}
~Printer() { flush(); }
int close() {
flush();
return ::close(fd);
}
void flush() {
if (pos) {
auto res = ::write(fd, line.data(), pos);
assert(res != -1);
pos = 0;
}
}
private:
static std::array<std::array<char, 2>, 100> small;
static std::array<unsigned long long, 20> tens;
static constexpr size_t SIZE = 1 << 15;
int fd;
std::array<char, SIZE> line;
size_t pos = 0;
std::stringstream ss;
template <class T,
std::enable_if_t<std::is_same<char, T>::value>* = nullptr>
void write_single(const T& val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T,
internal::is_signed_int_t<T>* = nullptr,
std::enable_if_t<!std::is_same<char, T>::value>* = nullptr>
void write_single(const T& val) {
using U = internal::to_unsigned_t<T>;
if (val == 0) {
write_single('0');
return;
}
if (pos > SIZE - 50) flush();
U uval = val;
if (val < 0) {
write_single('-');
uval = -uval;
}
write_unsigned(uval);
}
template <class U, internal::is_unsigned_int_t<U>* = nullptr>
void write_single(U uval) {
if (uval == 0) {
write_single('0');
return;
}
if (pos > SIZE - 50) flush();
write_unsigned(uval);
}
template <class U, internal::is_unsigned_int_t<U>* = nullptr>
static int calc_len(U x) {
int i = (bsr(x) * 3 + 3) / 10;
if (x < tens[i])
return i;
else
return i + 1;
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<2 >= sizeof(U)>* = nullptr>
void write_unsigned(U uval) {
size_t len = calc_len(uval);
pos += len;
char* ptr = line.data() + pos;
while (uval >= 100) {
ptr -= 2;
memcpy(ptr, small[uval % 100].data(), 2);
uval /= 100;
}
if (uval >= 10) {
memcpy(ptr - 2, small[uval].data(), 2);
} else {
*(ptr - 1) = char('0' + uval);
}
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<4 == sizeof(U)>* = nullptr>
void write_unsigned(U uval) {
std::array<char, 8> buf;
memcpy(buf.data() + 6, small[uval % 100].data(), 2);
memcpy(buf.data() + 4, small[uval / 100 % 100].data(), 2);
memcpy(buf.data() + 2, small[uval / 10000 % 100].data(), 2);
memcpy(buf.data() + 0, small[uval / 1000000 % 100].data(), 2);
if (uval >= 100000000) {
if (uval >= 1000000000) {
memcpy(line.data() + pos, small[uval / 100000000 % 100].data(),
2);
pos += 2;
} else {
line[pos] = char('0' + uval / 100000000);
pos++;
}
memcpy(line.data() + pos, buf.data(), 8);
pos += 8;
} else {
size_t len = calc_len(uval);
memcpy(line.data() + pos, buf.data() + (8 - len), len);
pos += len;
}
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<8 == sizeof(U)>* = nullptr>
void write_unsigned(U uval) {
size_t len = calc_len(uval);
pos += len;
char* ptr = line.data() + pos;
while (uval >= 100) {
ptr -= 2;
memcpy(ptr, small[uval % 100].data(), 2);
uval /= 100;
}
if (uval >= 10) {
memcpy(ptr - 2, small[uval].data(), 2);
} else {
*(ptr - 1) = char('0' + uval);
}
}
template <
class U,
std::enable_if_t<internal::is_unsigned_int128<U>::value>* = nullptr>
void write_unsigned(U uval) {
static std::array<char, 50> buf;
size_t len = 0;
while (uval > 0) {
buf[len++] = char((uval % 10) + '0');
uval /= 10;
}
std::reverse(buf.begin(), buf.begin() + len);
memcpy(line.data() + pos, buf.data(), len);
pos += len;
}
void write_single(const std::string& s) {
for (char c : s) write_single(c);
}
void write_single(const char* s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write_single(s[i]);
}
template <class T> void write_single(const std::vector<T>& val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write_single(' ');
write_single(val[i]);
}
}
};
std::array<std::array<char, 2>, 100> Printer::small = [] {
std::array<std::array<char, 2>, 100> table;
for (int i = 0; i <= 99; i++) {
table[i][1] = char('0' + (i % 10));
table[i][0] = char('0' + (i / 10 % 10));
}
return table;
}();
std::array<unsigned long long, 20> Printer::tens = [] {
std::array<unsigned long long, 20> table;
for (int i = 0; i < 20; i++) {
table[i] = 1;
for (int j = 0; j < i; j++) {
table[i] *= 10;
}
}
return table;
}();
} // namespace yosupo
#include <array>
#include <cassert>
#include <chrono>
#include <cstdint>
#include <type_traits>
namespace yosupo {
struct Xoshiro256StarStar {
public:
using result_type = uint64_t;
Xoshiro256StarStar() : Xoshiro256StarStar(0) {}
explicit Xoshiro256StarStar(uint64_t seed) {
for (int i = 0; i < 4; i++) {
uint64_t z = (seed += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
s[i] = z ^ (z >> 31);
}
}
static constexpr result_type min() { return 0; }
static constexpr result_type max() { return -1; }
result_type operator()() {
const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9;
const uint64_t t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 45);
return result_starstar;
}
private:
static uint64_t rotl(const uint64_t x, int k) {
return (x << k) | (x >> (64 - k));
}
std::array<uint64_t, 4> s;
};
namespace internal {
template <class G> uint64_t uniform(uint64_t upper, G& gen) {
static_assert(std::is_same<uint64_t, typename G::result_type>::value, "");
static_assert(G::min() == 0, "");
static_assert(G::max() == uint64_t(-1), "");
if (!(upper & (upper + 1))) {
return gen() & upper;
}
int log = bsr(upper);
uint64_t mask = (log == 63) ? ~0ULL : (1ULL << (log + 1)) - 1;
while (true) {
uint64_t r = gen() & mask;
if (r <= upper) return r;
}
}
} // namespace internal
Xoshiro256StarStar& global_gen() {
static Xoshiro256StarStar gen(
std::chrono::steady_clock::now().time_since_epoch().count());
return gen;
}
template <class T, class G> T uniform(T lower, T upper, G& gen) {
return T(lower + internal::uniform(uint64_t(upper) - uint64_t(lower), gen));
}
template <class T> T uniform(T lower, T upper) {
return uniform(lower, upper, global_gen());
}
template <class G> bool uniform_bool(G& gen) {
return internal::uniform(1, gen) == 1;
}
bool uniform_bool() { return uniform_bool(global_gen()); }
template <class T, class G>
std::pair<T, T> uniform_pair(T lower, T upper, G& gen) {
assert(upper - lower >= 1);
T a, b;
do {
a = uniform(lower, upper, gen);
b = uniform(lower, upper, gen);
} while (a == b);
if (a > b) std::swap(a, b);
return {a, b};
}
template <class T> std::pair<T, T> uniform_pair(T lower, T upper) {
return uniform_pair(lower, upper, global_gen());
}
} // namespace yosupo
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <iostream>
namespace atcoder {
template <int MOD>
std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) {
return os << x.val();
}
template <int ID>
std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) {
return os << x.val();
}
} // namespace atcoder
namespace yosupo {
template <int MOD> using static_modint = atcoder::static_modint<MOD>;
template <int ID> using dynamic_modint = atcoder::dynamic_modint<ID>;
using modint998244353 = atcoder::modint998244353;
using modint1000000007 = atcoder::modint1000000007;
using modint = atcoder::modint;
} // namespace yosupo
using namespace yosupo;
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <complex>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
#ifdef LOCAL
ostream& operator<<(ostream& os, __int128_t x) {
if (x < 0) {
os << "-";
x *= -1;
}
if (x == 0) {
return os << "0";
}
string s;
while (x) {
s += char(x % 10 + '0');
x /= 10;
}
reverse(s.begin(), s.end());
return os << s;
}
ostream& operator<<(ostream& os, __uint128_t x) {
if (x == 0) {
return os << "0";
}
string s;
while (x) {
s += char(x % 10 + '0');
x /= 10;
}
reverse(s.begin(), s.end());
return os << s;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> ostream& operator<<(ostream& os, const V<T>& v);
template <class T> ostream& operator<<(ostream& os, const deque<T>& v);
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T> ostream& operator<<(ostream& os, const set<T>& s);
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& m);
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
return os << "P(" << p.first << ", " << p.second << ")";
}
template <class T> ostream& operator<<(ostream& os, const V<T>& v) {
os << "[";
bool f = false;
for (auto d : v) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "]";
}
template <class T> ostream& operator<<(ostream& os, const deque<T>& v) {
os << "[";
bool f = false;
for (auto d : v) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "]";
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
os << "[";
bool f = false;
for (auto d : a) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "]";
}
template <class T> ostream& operator<<(ostream& os, const set<T>& s) {
os << "{";
bool f = false;
for (auto d : s) {
if (f) os << ", ";
f = true;
os << d;
}
return os << "}";
}
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& s) {
os << "{";
bool f = false;
for (auto p : s) {
if (f) os << ", ";
f = true;
os << p.first << ": " << p.second;
}
return os << "}";
}
struct PrettyOS {
ostream& os;
bool first;
template <class T> auto operator<<(T&& x) {
if (!first) os << ", ";
first = false;
os << x;
return *this;
}
};
template <class... T> void dbg0(T&&... t) {
(PrettyOS{cerr, true} << ... << t);
}
#define dbg(...) \
do { \
cerr << __LINE__ << " : " << #__VA_ARGS__ << " = "; \
dbg0(__VA_ARGS__); \
cerr << endl; \
} while (false);
#else
#define dbg(...)
#endif
struct Nimber64;
Nimber64 mul_naive(Nimber64 l, Nimber64 r);
struct Nimber64 {
const static V<ull> factor;
const static array<array<unsigned char, 256>, 256> small;
const static array<array<array<Nimber64, 256>, 8>, 8> precalc;
ull v;
Nimber64() : v(0) {}
Nimber64(ull _v) : v(_v) {}
const Nimber64 operator+(Nimber64 r) const { return v ^ r.v; }
const Nimber64 operator-(Nimber64 r) const { return v ^ r.v; }
const Nimber64 operator*(Nimber64 r) const {
Nimber64 ans;
for (int i = 0; i < 8; i++) {
for (int j = 0; j < 8; j++) {
ull x = (v >> (8 * i)) % 256;
ull y = (r.v >> (8 * j)) % 256;
ans += precalc[i][j][small[x][y]];
}
}
return ans;
}
const Nimber64 operator/(Nimber64 r) const {
auto ri = r.pow(ull(-1) - 1);
assert((r * ri) == Nimber64(1));
return (*this) * ri;
}
bool operator==(Nimber64 r) const { return v == r.v; }
bool operator!=(Nimber64 r) const { return v != r.v; }
Nimber64& operator+=(Nimber64 r) { return *this = *this + r; }
Nimber64& operator-=(Nimber64 r) { return *this = *this - r; }
Nimber64& operator*=(Nimber64 r) { return *this = *this * r; }
Nimber64& operator/=(Nimber64 r) { return *this = *this / r; }
Nimber64 pow(ull n) const {
Nimber64 x = *this, r = 1;
while (n) {
if (n & 1) r = r * x;
x = x * x;
n >>= 1;
}
return r;
}
ull discrete_logarithm(Nimber64 y) {
ull rem = 0, mod = 1;
for (ull p : factor) {
ull STEP = 1;
while (4 * STEP * STEP < p) STEP *= 2;
auto inside = [&](Nimber64 x, Nimber64 z) {
unordered_map<ull, int> mp;
Nimber64 big = 1; // x^m
for (int i = 0; i < int(STEP); i++) {
mp[z.v] = i;
z *= x;
big *= x;
}
Nimber64 now = 1;
for (ull step = 0; step < ull(p + 10); step += STEP) {
now *= big;
// check [step + 1, step + STEP]
if (mp.find(now.v) != mp.end()) {
return (step + STEP) - mp[now.v];
}
}
return ull(-1);
};
ull q = ull(-1) / p;
ull res = inside((*this).pow(q), y.pow(q));
if (res == ull(-1)) {
return ull(-1);
}
res %= p;
// mod p = v
if (mod == 1) {
rem = res;
mod = p;
} else {
while (rem % p != res) rem += mod;
mod *= p;
}
}
return rem;
}
bool is_primitive_root() const {
for (ull p : factor) {
if ((*this).pow(ull(-1) / p).v == 1) return false;
}
return true;
}
};
const V<ull> Nimber64::factor = {
6700417, 65537, 641, 257, 17, 5, 3,
};
Nimber64 mul_naive(Nimber64 l, Nimber64 r) {
ull a = l.v, b = r.v;
if (a < b) swap(a, b);
if (b == 0) return 0;
if (b == 1) return a;
int p = 32;
while (max(a, b) < (1ULL << p)) p /= 2;
ull power = 1ULL << p;
if (a >= power && b >= power) {
Nimber64 ans;
ans += mul_naive(a % power, b % power);
ans += mul_naive(a / power, b % power).v * power;
ans += mul_naive(a % power, b / power).v * power;
auto x = mul_naive(a / power, b / power);
ans += x.v * power;
ans += mul_naive(x.v, power / 2);
return ans;
} else {
return Nimber64(mul_naive(a / power, b).v * power) +
mul_naive(a % power, b);
}
};
const array<array<unsigned char, 256>, 256> Nimber64::small = []() {
array<array<unsigned char, 256>, 256> small;
for (int i = 0; i < 256; i++) {
for (int j = 0; j < 256; j++) {
small[i][j] = (unsigned char)(mul_naive(i, j).v);
}
}
return small;
}();
const array<array<array<Nimber64, 256>, 8>, 8> Nimber64::precalc = []() {
array<array<array<Nimber64, 256>, 8>, 8> precalc;
for (int i = 0; i < 8; i++) {
for (int j = 0; j < 8; j++) {
for (int k = 0; k < 256; k++) {
precalc[i][j][k] =
mul_naive(mul_naive(1ULL << (8 * i), 1ULL << (8 * j)), k);
}
}
}
return precalc;
}();
template <class D> struct Mat : VV<D> {
using VV<D>::VV;
using VV<D>::size;
int h() const { return int(size()); }
int w() const { return int((*this)[0].size()); }
Mat operator*(const Mat& r) const {
assert(w() == r.h());
Mat res(h(), V<D>(r.w()));
for (int i = 0; i < h(); i++) {
for (int j = 0; j < r.w(); j++) {
for (int k = 0; k < w(); k++) {
res[i][j] += (*this)[i][k] * r[k][j];
}
}
}
return res;
}
Mat& operator*=(const Mat& r) { return *this = *this * r; }
Mat pow(ll n) const {
assert(h() == w());
Mat x = *this, r(h(), V<D>(w()));
for (int i = 0; i < h(); i++) r[i][i] = D(1);
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
};
template <class Mint> int calc_rank(Mat<Mint> a) {
int h = a.h(), w = a.w();
int r = 0;
V<int> idxs;
for (int x = 0; x < w; x++) {
int my = -1;
for (int y = r; y < h; y++) {
if (a[y][x] != Mint(0)) {
my = y;
break;
}
}
if (my == -1) continue;
if (r != my) swap(a[r], a[my]);
for (int y = r + 1; y < h; y++) {
if (a[y][x] == Mint(0)) continue;
auto freq = a[y][x] / a[r][x];
for (int k = x; k < w; k++) a[y][k] -= freq * a[r][k];
}
r++;
idxs.push_back(x);
if (r == h) break;
}
return r;
}
Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);
int main() {
int n, m;
sc.read(n, m);
Mat<modint998244353> mat(n, V<modint998244353>(n));
for (int i = 0; i < m; i++) {
int a, b, c;
sc.read(a, b, c);
a--; b--; c--;
modint998244353 x = uniform(0, 998244352);
// (a, b) = (1, -1)
// (b, c) = (1, -1)
mat[a][b] += x;
mat[b][b] -= x;
mat[a][c] -= x;
mat[b][c] += x;
mat[b][a] -= x;
mat[c][a] += x;
mat[b][b] += x;
mat[c][b] -= x;
}
int ans = calc_rank(mat);
pr.writeln(ans / 2);
return 0;
}