#721941 (C++17) No.1773 Love Triangle

提出ソース

結果

問題	No.1773 Love Triangle
ユーザー	hotman78
提出日時	2021-12-05 10:37:26
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,123 ms / 2,000 ms
コード長	26,410 bytes
コンパイル時間	4,060 ms
コンパイル使用メモリ	258,224 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-07 07:06:22
合計ジャッジ時間	55,994 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

このコードへのチャレンジ
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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	2 ms 6,816 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	3 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	3 ms 6,940 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	1 ms 6,944 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	3 ms 6,940 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	1 ms 6,940 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,944 KB
testcase_16	AC	1 ms 6,940 KB
testcase_17	AC	3 ms 6,944 KB
testcase_18	AC	707 ms 6,944 KB
testcase_19	AC	5 ms 6,940 KB
testcase_20	AC	31 ms 6,940 KB
testcase_21	AC	2 ms 6,940 KB
testcase_22	AC	30 ms 6,940 KB
testcase_23	AC	25 ms 6,944 KB
testcase_24	AC	114 ms 6,940 KB
testcase_25	AC	207 ms 6,944 KB
testcase_26	AC	2 ms 6,940 KB
testcase_27	AC	3 ms 6,940 KB
testcase_28	AC	4 ms 6,944 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	541 ms 6,940 KB
testcase_31	AC	195 ms 6,940 KB
testcase_32	AC	45 ms 6,944 KB
testcase_33	AC	5 ms 6,940 KB
testcase_34	AC	3 ms 6,944 KB
testcase_35	AC	6 ms 6,940 KB
testcase_36	AC	96 ms 6,944 KB
testcase_37	AC	2 ms 6,944 KB
testcase_38	AC	1,027 ms 6,940 KB
testcase_39	AC	1,018 ms 6,940 KB
testcase_40	AC	1,012 ms 6,944 KB
testcase_41	AC	1,045 ms 6,944 KB
testcase_42	AC	1,078 ms 6,940 KB
testcase_43	AC	1,053 ms 6,940 KB
testcase_44	AC	1,067 ms 6,940 KB
testcase_45	AC	1,041 ms 6,944 KB
testcase_46	AC	1,083 ms 6,944 KB
testcase_47	AC	1,045 ms 6,944 KB
testcase_48	AC	1,074 ms 6,944 KB
testcase_49	AC	1,081 ms 6,944 KB
testcase_50	AC	1,035 ms 6,944 KB
testcase_51	AC	1,034 ms 6,940 KB
testcase_52	AC	1,023 ms 6,940 KB
testcase_53	AC	1,047 ms 6,940 KB
testcase_54	AC	1,020 ms 6,940 KB
testcase_55	AC	1,036 ms 6,940 KB
testcase_56	AC	1,010 ms 6,940 KB
testcase_57	AC	1,015 ms 6,940 KB
testcase_58	AC	1,073 ms 6,940 KB
testcase_59	AC	1,080 ms 6,940 KB
testcase_60	AC	1,095 ms 6,940 KB
testcase_61	AC	1,090 ms 6,944 KB
testcase_62	AC	1,050 ms 6,940 KB
testcase_63	AC	1,075 ms 6,940 KB
testcase_64	AC	1,084 ms 6,940 KB
testcase_65	AC	1,080 ms 6,944 KB
testcase_66	AC	1,066 ms 6,940 KB
testcase_67	AC	1,067 ms 6,940 KB
testcase_68	AC	1,087 ms 6,940 KB
testcase_69	AC	1,058 ms 6,944 KB
testcase_70	AC	1,104 ms 6,940 KB
testcase_71	AC	1,097 ms 6,940 KB
testcase_72	AC	1,088 ms 6,944 KB
testcase_73	AC	1,092 ms 6,944 KB
testcase_74	AC	1,070 ms 6,944 KB
testcase_75	AC	1,102 ms 6,940 KB
testcase_76	AC	1,123 ms 6,940 KB
testcase_77	AC	1,103 ms 6,944 KB
testcase_78	AC	2 ms 6,940 KB
testcase_79	AC	1 ms 6,940 KB
testcase_80	AC	11 ms 6,940 KB
testcase_81	AC	1,084 ms 6,944 KB
testcase_82	AC	1,067 ms 6,940 KB
testcase_83	AC	234 ms 6,944 KB
testcase_84	AC	352 ms 6,940 KB
testcase_85	AC	528 ms 6,944 KB
testcase_86	AC	88 ms 6,940 KB
testcase_87	AC	271 ms 6,940 KB
testcase_88	AC	22 ms 6,940 KB
testcase_89	AC	183 ms 6,944 KB
testcase_90	AC	807 ms 6,944 KB
testcase_91	AC	521 ms 6,940 KB
testcase_92	AC	56 ms 6,940 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#line 2 "cpplib/util/template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#include<bits/stdc++.h>
using namespace std;
struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}}__INIT__;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define endl ('\n')
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>using V=vector<T>;
template<typename T>using VV=V<V<T>>;
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<<i;f=1;}cerr<<endl;}
template<typename T>inline void debug2(T t){for(auto i:t)debug(i);}
#define loop(n) for(long long _=0;_<(long long)(n);++_)
#define _overload4(_1,_2,_3,_4,name,...) name
#define __rep(i,a) repi(i,0,a,1)
#define _rep(i,a,b) repi(i,a,b,1)
#define repi(i,a,b,c) for(long long i=(long long)(a);i<(long long)(b);i+=c)
#define rep(...) _overload4(__VA_ARGS__,repi,_rep,__rep)(__VA_ARGS__)
#define _overload3_rev(_1,_2,_3,name,...) name
#define _rep_rev(i,a) repi_rev(i,0,a)
#define repi_rev(i,a,b) for(long long i=(long long)(b)-1;i>=(long long)(a);--i)
#define rrep(...) _overload3_rev(__VA_ARGS__,repi_rev,_rep_rev)(__VA_ARGS__)

// #define rep(i,...) for(auto i:range(__VA_ARGS__)) 
// #define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
// #define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
// #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
// #define irep(i) for(lint i=0;;++i)
// inline vector<long long> range(long long n){if(n<=0)return vector<long long>();vector<long long>v(n);iota(v.begin(),v.end(),0LL);return v;}
// inline vector<long long> range(long long a,long long b){if(b<=a)return vector<long long>();vector<long long>v(b-a);iota(v.begin(),v.end(),a);return v;}
// inline vector<long long> range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector<long long>();vector<long long>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
// template<typename T>inline T reversed(T v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
template<typename T,typename E>bool chmin(T& s,const E& t){bool res=s>t;s=min<T>(s,t);return res;}
template<typename T,typename E>bool chmax(T& s,const E& t){bool res=s<t;s=max<T>(s,t);return res;}
const string ds="DRUL";
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
#if __cplusplus>=201703L
    template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
#endif
#define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__}))
#define bit(n,a) ((n>>a)&1)
vector<vector<long long>> __MAKE_MAT__(vector<long long> v){if(v.empty())return vector<vector<long long>>(1,vector<long long>());long long n=v.back();v.pop_back();vector<vector<long long>> ret;vector<vector<long long>> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i<n;++i){ret.push_back(e);ret.back().push_back(i);}return ret;}
using graph=vector<vector<int>>;
template<typename T>using graph_w=vector<vector<pair<int,T>>>;
template<typename T,typename E>ostream& operator<<(ostream& out,pair<T,E>v){out<<"("<<v.first<<","<<v.second<<")";return out;}
#if __cplusplus>=201703L
    constexpr inline long long powll(long long a,long long b){long long res=1;while(b--)res*=a;return res;}
#endif

template<typename T,typename E>pair<T,E>& operator+=(pair<T,E>&s,const pair<T,E>&t){s.first+=t.first;s.second+=t.second;return s;}
template<typename T,typename E>pair<T,E>& operator-=(pair<T,E>&s,const pair<T,E>&t){s.first-=t.first;s.second-=t.second;return s;}
template<typename T,typename E>pair<T,E> operator+(const pair<T,E>&s,const pair<T,E>&t){auto res=s;return res+=t;}
template<typename T,typename E>pair<T,E> operator-(const pair<T,E>&s,const pair<T,E>&t){auto res=s;return res-=t;}
#define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024));
#define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_);
#line 2 "cpplib/math/ACL_modint998244353.hpp"

#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

using mint=atcoder::modint998244353;
#line 4 "cpplib/math/ACL_modint_base.hpp"

std::ostream& operator<<(std::ostream& lhs, const mint& rhs) noexcept {
    lhs << rhs.val();
    return lhs;
}
std::istream& operator>>(std::istream& lhs,mint& rhs) noexcept {
    long long x;
    lhs >> x;
    rhs=x;
    return lhs;
}

int MOD_NOW=-1;
int sz=0;
std::vector<mint>fact_table,fact_inv_table;

void update(int x){
    if(MOD_NOW!=mint::mod()||sz==0){
        fact_table.assign(1,1);
        fact_inv_table.assign(1,1);
        sz=1;
        MOD_NOW=mint::mod();
    }
    while(sz<=x){
        fact_table.resize(sz*2);
        fact_inv_table.resize(sz*2);
        for(int i=sz;i<sz*2;++i){
            fact_table[i]=fact_table[i-1]*i;
        }
        fact_inv_table[sz*2-1]=fact_table[sz*2-1].inv();
        for(int i=sz*2-2;i>=sz;--i){
            fact_inv_table[i]=fact_inv_table[i+1]*(i+1);
        }
        sz*=2;
    }
}

inline mint fact(int x){
    assert(x>=0);
    update(x);
    return fact_table[x];
}
inline mint fact_inv(int x){
    assert(x>=0);
    update(x);
    return fact_inv_table[x];
}
inline mint comb(int x,int y){
    if(x<0||x<y||y<0)return 0;
    return fact(x)*fact_inv(y)*fact_inv(x-y);
}
inline mint perm(int x,int y){
    return fact(x)*fact_inv(y);
}
inline mint multi_comb(int x,int y){
    return comb(x+y-1,y);
}
#line 3 "main.cpp"

int main(){
    // タスケテー
    int n,m;
    cin>>n>>m;
    vector<tuple<lint,lint,lint>>pp(m);
    vec s;
    rep(i,m){
        lint p,q,r;
        cin>>p>>q>>r;
        p--;q--;r--;
        pp[i]=make_tuple(p,q,r);
        s.emplace_back(p);
        s.emplace_back(q);
        s.emplace_back(r);
    }
    sort(all(s));
    s.erase(unique(all(s)),s.end());
    map<tuple<lint,lint,lint>,lint>M;
    using mat=vector<vector<mint>>;
    using vec=vector<mint>;
    n=s.size();
    mat Y(n,vec(n));
    random_device rnd;
    auto idx=[&](lint x){
        return lower_bound(all(s),x)-s.begin();
    };
    for(auto [p,q,r]:pp){
        lint tmp=rnd();
        M[make_tuple(p,q,r)]=tmp;
        Y[idx(p)][idx(q)]+=tmp;
        Y[idx(q)][idx(p)]-=tmp;

        Y[idx(r)][idx(p)]+=tmp;
        Y[idx(p)][idx(r)]-=tmp;

        Y[idx(r)][idx(q)]-=tmp;
        Y[idx(q)][idx(r)]+=tmp;
    }
    // auto mul=[&](const auto& s,const auto& t){
    //     assert(s[0].size()==t.size());
    //     mat res(s.size(),vec(t[0].size()));
    //     rep(i,s.size())rep(j,s[0].size())rep(k,t[0].size()){
    //         res[i][k]+=s[i][j]*t[j][k];
    //     }
    //     return res;
    // };
    // auto add_I=[&](const auto& s){
    //     auto res=s;
    //     rep(i,s.size()){
    //         res[i][i]++;
    //     }
    //     return res;
    // };
    // auto det=[&](const auto& s)->mint{
    //     assert(s.size()==3);
    //     mint res=0;
    //     rep(i,3){
    //         mint tmp=1;
    //         rep(j,3){
    //             tmp*=s[i][(i+j)%3];
    //         }
    //         res+=tmp;
    //     }
    //     rep(i,3){
    //         mint tmp=1;
    //         rep(j,3){
    //             tmp*=s[i][(i-j+3)%3];
    //         }
    //         res-=tmp;
    //     }
    //     return res;
    // };
    auto rank=[&](auto s){
        int n=s.size();
        auto sw=[&](int i,int j){
            rep(k,n){
                swap(s[i][k],s[j][k]);
            }
        };
        auto minus=[&](int i,int j,mint x){
            rep(k,n){
                s[i][k]-=s[j][k]*x;
            }
        };
        auto mul=[&](int i,mint x){
            rep(k,n){
                s[i][k]*=x;
            }
        };
        int r=0;
        int res=n;
        rep(i,n){
            rep(j,r+1,n){
                if(s[r][i]!=mint(0))break;
                if(s[j][i]!=mint(0)){
                    sw(r,j);
                }
            }
            if(s[r][i]==mint(0)){
                res--;
                continue;
            }
            mul(r,s[r][i].inv());
            rep(j,n){
                if(r!=j){
                    minus(j,r,s[j][i]);
                }
            }
            r++;
        }
        // debug2(s);
        return res;
    };
    auto ans=rank(Y);
    // cerr<<Y.size()<<endl;
    // cerr<<ans<<endl;
    cout<<ans/2<<endl;
    // auto f=[&](auto f,mat N,int l1,int r1,int l2,int r2,int l3,int r3)->mat{
    //     vector<lint>s;
    //     rep(i,l1,r1)s.emplace_back(i);
    //     rep(i,l2,r2)s.emplace_back(i);
    //     rep(i,l3,r3)s.emplace_back(i);
    //     sort(all(s));
    //     s.erase(unique(all(s)),s.end());
    //     mat res(s.size(),vec(s.size()));
    //     if(r1-l1==1&&r2-l2==1&&r3-l3==1){
    //         mat D(3,vec(3,0));
    //         if(M.count({l1,l2,l3})){
    //             lint tmp=M[{l1,l2,l3}];
    //             mat NS(3,vec(3,0));
    //             vector<int> v={l1,l2,l3};
    //             D[0][1]-=tmp;
    //             D[1][0]-=tmp;
    //             D[0][2]-=tmp;
    //             D[2][0]-=tmp;
    //             auto detr=det(add_I(mul(D,N)));
    //             // debug2(add_I(mul(D,N)));
    //             // cerr<<detr<<endl;
    //             if(detr!=mint(0)){
    //                 Y[l1][l2]-=tmp;
    //                 Y[l3][l1]-=tmp;
    //                 Y[l3][l2]-=tmp;
    //                 Y[l1][l3]+=tmp;
    //                 Y[l2][l1]+=tmp;
    //                 Y[l2][l3]+=tmp;
    //                 ans--;
    //             }
    //             return D;
    //         }
    //     }else{
    //         int m1=(l1+r1)/2;
    //         int m2=(l2+r2)/2;
    //         int m3=(l3+r3)/2;
    //         for(auto p1:{pair{l1,m1},pair{m1,r1}})for(auto p2:{pair{l2,m2},pair{m2,r2}})for(auto p3:{pair{l3,m3},pair{m3,r3}}){
    //             if(p1.first==p1.second)continue;
    //             if(p2.first==p2.second)continue;
    //             if(p3.first==p3.second)continue;
    //             vector<lint>s2;
    //             rep(i,p1.first,p1.second)s2.emplace_back(i);
    //             rep(i,p2.first,p2.second)s2.emplace_back(i);
    //             rep(i,p3.first,p3.second)s2.emplace_back(i);
    //             sort(all(s2));
    //             s2.erase(unique(all(s2)),s2.end());

    //             mat NTS(s.size(),vec(s2.size())),NST(s2.size(),vec(s.size())),NS(s2.size(),vec(s2.size()));
    //             rep(i,s2.size())rep(j,s2.size()){
    //                 NS[i][j]=N[lower_bound(all(s),s2[i])-s.begin()][lower_bound(all(s),s2[j])-s.begin()];
    //             }
    //             auto D=f(f,NS,p1.first,p1.second,p2.first,p2.second,p3.first,p3.second);
    //             rep(i,s2.size())rep(j,s2.size()){
    //                 res[lower_bound(all(s),s2[i])-s.begin()][lower_bound(all(s),s2[j])-s.begin()]
    //                     +=D[i][j];
    //             }
    //             rep(i,s.size())rep(j,s2.size()){
    //                 NTS[i][j]=N[s[i]][s2[j]];
    //             }
    //             rep(i,s2.size())rep(j,s.size()){
    //                 NST[i][j]=N[s2[i]][s[j]];
    //             }
    //             auto tmp=mul(mul(mul(NTS,inv(add_I(mul(D,NS)))),D),NST);
    //             rep(i,s.size())rep(j,s.size()){
    //                 N[i][j]-=tmp[i][j];
    //             }
    //         }
    //     }
    //     return res;
    // };
    // f(f,N,0,n,0,n,0,n);
    // cout<<ans<<endl;
}

yukicoder

結果

テストケース

ソースコード