結果

問題 No.2985 May Count Induced C4 Subgraphs
ユーザー 👑 p-adicp-adic
提出日時 2024-12-11 16:10:22
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 50,822 bytes
コンパイル時間 5,453 ms
コンパイル使用メモリ 275,720 KB
実行使用メモリ 98,644 KB
最終ジャッジ日時 2024-12-11 16:11:38
合計ジャッジ時間 66,084 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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
47,152 KB
testcase_01 AC 2 ms
47,120 KB
testcase_02 AC 2 ms
10,496 KB
testcase_03 AC 2 ms
46,948 KB
testcase_04 AC 2 ms
10,624 KB
testcase_05 AC 2 ms
46,968 KB
testcase_06 TLE -
testcase_07 TLE -
testcase_08 TLE -
testcase_09 TLE -
testcase_10 TLE -
testcase_11 TLE -
testcase_12 AC 466 ms
53,360 KB
testcase_13 AC 456 ms
53,368 KB
testcase_14 AC 455 ms
53,364 KB
testcase_15 AC 450 ms
53,364 KB
testcase_16 AC 480 ms
53,372 KB
testcase_17 AC 3,900 ms
51,116 KB
testcase_18 AC 4,728 ms
51,208 KB
testcase_19 TLE -
testcase_20 AC 2,846 ms
51,240 KB
testcase_21 AC 3,297 ms
98,644 KB
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ソースコード

diff # 

#ifndef INCLUDE_MODE
  #define INCLUDE_MODE
  // #define REACTIVE
  // #define USE_GETLINE
  #define SUBMIT_ONLY
  #define DEBUG_OUTPUT
  #define SAMPLE_CHECK I
#endif
#ifdef INCLUDE_MAIN

// 公式解説やSSRSさんの記事には先行研究の引用がないので、
// 先行研究にアクセスしやすいようにある程度リファレンスがまとまっている文献を載せる：
// [1] Mark Ortmann and Ulrik Brandes,
//     Efficient orbit-aware triad and quad census in directed and undirected graphs,
//     OrtmannandBrandesAppliedNetworkScience (2017) 2:13
// 頂点や辺の被覆回数をもとにnon-inducedやinduced subgraphの個数に関する線形関係式を
// 与える手法や、それにより上からの計算量解析が可能であることも述べられている。

// 公式解説はnon-induced C_nをC_nと書いているので注意。
VO Solve()
{
  CIN( int , N , M );
  vector<T2<int>> e_dir( M );
  vector<int> degree( N );
  FOR( m , 0 , M ){
    CIN( int , i , j ); --i; --j;
    e_dir[m] = {i,j};
    degree[i]++;
    degree[j]++;
  }
  // Norishige Chiba and Takao Nishizeki 
  // [2] Arboricity and subgraph listing algorithms,
  //     SIAM J. Comput. 14(1):210--223.
  // のCOMPLETEアルゴリズムの3頂点版（O(a(G)|E|)）を用いる。
  // より正確には[1]のAlgorithm 1でK3とnon-induced C4を同時に計算。
  vector<vector<int>> e( N );
  vector<vector<int>> e_plus( N );
  vector<vector<int>> e_minus( N );
  auto order = [&]( const int& i , const int& j ){
    return T2<int>{degree[i],i} < T2<int>{degree[j],j};
  };
  Map<T2<int>,int> e_dir_inv{};
  FOR( m , 0 , M ){
    auto& [i,j] = e_dir[m];
    if( !order( i , j ) ){
      swap( i , j );
    }
    e_dir_inv[{i,j}] = m;
    e[i].push_back( j );
    e[j].push_back( i );
    e_plus[i].push_back( j );
    e_minus[j].push_back( i );
  }
  FOR( i , 0 , N ){
    // [1]ではバケットソートしているが、オーダーレベルでは変わらない。
    sort( e[i].begin() , e[i].end() , order );
    sort( e_plus[i].begin() , e_plus[i].end() , order );
    sort( e_minus[i].begin() , e_minus[i].end() , order );
  }
  vector<int> coord = id<int>( N );
  sort( coord.begin() , coord.end() , order );
  vector<int> mark( N ) , visited( N ) , processed( N );
  int K3 = 0; // K3を数え上げ。
  vector<ll> marked_K3( M ); // 1辺がマークされたK3を数え上げ。
  ll niC3_1 = 0; // non-induced |>-の字を数え上げ。
  ll niC4 = 0; // non-induced C4を数え上げ。
  RUN( coord , i ){
    RUN( e_minus[i] , j ){
      mark[j]++; // iから1歩で行けてかつチェック1前か否かを管理。
      assert( mark[j] == 1 );
    }
    RUN( e_minus[i] , j ){
      RUN( e[j] , k ){
        if( !order( k , i ) ){
          break;
        }
        visited[k]++; // iから2歩で行く経路であってorderがi以下なものを数える。
        processed[k]++; // 上記経路について纏めて１回だけ処理するためのカウンタ。
      }
      RUN( e_plus[j] , k ){
        if( !order( k , i ) ){
          break;
        }
        mark[k] += 2; // jから1歩で行けてかつorderが(j,i)の間かつチェック2前かも2進法で管理。
      }
      RUN( e_plus[j] , k ){
        if( !order( k , i ) ){
          break;
        }
        if( mark[k] == 3 ){ // iからも1歩で行けるケース。
          K3++; // (j,k,i)がorder順かつK3をなす。
          niC3_1 += degree[j] + degree[k] + degree[i] - 6;
          marked_K3[e_dir_inv[{j,k}]]++;
          marked_K3[e_dir_inv[{k,i}]]++;
          marked_K3[e_dir_inv[{j,i}]]++;
          // K4も数える場合は以下を処理してO(a(G)^2|E|)となる。
          // RUN( e_plus[k] , l ){
          //   if( !order( l , i ) ){
          //     break;
          //   }
          //   if( mark[l] == 3 ){
          //     K4++; // (j,k,l,i)がorder順かつK4をなす。
          //   }
          // }
        } else {
          assert( mark[k] == 2 );
        }
        mark[k] -= 2; // チェック2。(j,k,i)がorder順かつK3をなすものの探索終了。
      }
      mark[j]--; // チェック1。(j,*,i)がorder順かつK3をなすものの探索終了。
      assert( mark[j] == 0 );
    }
    RUN( e_minus[i] , j ){
      RUN( e[j] , k ){
        if( !order( k , i ) ){
          break;
        }
        processed[k]--;
        if( processed[k] == 0 ){ // カウンタのおかげでkごとに１回だけ処理される。
          niC4 += visited[k] * ( visited[k] - 1 ) / 2; // iから2歩で行く経路であってorderがi以下のものを2つ選ぶ。
          visited[k] = 0; // 今回はこの処理は不要だが入れておく。
          // これで{k,*,*,i}がC4をなすものであって(k,i)に辺がなくiがorder順で最大のものを数え上げたことになる。
        }
        // non-induced C4の単純な個数ではなく頂点や辺ごとの被覆回数を求める時は
        // ここに更に処理を行う。
      }
    }
  }
  CERR( "K3 =" , K3 );
  CERR( "niC3_1 =" , niC3_1 );
  CERR( "niC4 =" , niC3_1 );
  // 後は公式解説の通り線形関係式を解くだけ。
  vector<vector<MP>> A =
    {
      { 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 } ,
      { 0 , 1 , 2 , 2 , 3 , 3 , 3 , 4 , 4 , 5 , 6 } ,
      { 0 , 0 , 1 , 0 , 3 , 2 , 3 , 4 , 5 , 8 , 12 } ,
      { 0 , 0 , 0 , 1 , 0 , 1 , 0 , 2 , 1 , 2 , 3 } ,
      { 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 1 , 2 , 4 } ,
      { 0 , 0 , 0 , 0 , 0 , 1 , 0 , 4 , 2 , 6 , 12 } ,
      { 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 1 , 2 , 4 } ,
      { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 1 , 3 } ,
      { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 4 , 12 } ,
      { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 6 }
    };
  A[0].push_back( MP::Combination( N , 4 ) ); // non-induced coK4を数え上げ。
  A[1].push_back( N > 1 ? M * MP::Combination( N - 2 , 2 ) : MP::zero() ); // non-induced÷の字を数え上げ。
  MP deg2{} , deg3{};
  FOR( i , 0 , N ){
    deg2 += MP::Combination( degree[i] , 2 );
    deg3 += MP::Combination( degree[i] , 3 );
  }
  A[2].push_back( ( N - 3 ) * deg2 ); // non-induced Γ.の字を数え上げ。
  A[3].push_back( MP::Combination( M , 2 ) - deg2 ); // non-inducedニの字を数え上げ。
  A[4].push_back( deg3 ); // non-induced Yの字を数え上げ。
  MP co = -3 * K3;
  FOR( m , 0 , M ){
    auto& [i,j] = e_dir[m];
    co += MP( degree[i] - 1 ) * ( degree[j] - 1 );
  }
  A[5].push_back( co ); // non-inducedコの字を数え上げ。
  A[6].push_back( MP( N - 3 ) * K3 ); // non-induced △.の字を数え上げ。
  A[7].push_back( niC4 ); // non-induced C4を数え上げ。
  A[8].push_back( niC3_1 ); // non-induced |>-の字を数え上げ。
  MP nichi{};
  FOR( m , 0 , M ){
    nichi += MP::Combination( marked_K3[m] , 2 );
  }
  A[9].push_back( nichi ); // non-induced <|>の字を数え上げ。
  CERR( A[0] ); // non-induced coK4を数え上げ。
  CERR( A[1] ); // non-induced÷の字を数え上げ。
  CERR( A[2] ); // non-induced Γ.の字を数え上げ。
  CERR( A[3] ); // non-inducedニの字を数え上げ。
  CERR( A[4] ); // non-induced Yの字を数え上げ。
  CERR( A[5] ); // non-inducedコの字を数え上げ。
  CERR( A[6] ); // non-induced △.の字を数え上げ。
  CERR( A[7] ); // non-induced C4を数え上げ。
  CERR( A[8] ); // non-induced |>-の字を数え上げ。
  CERR( A[9] ); // non-induced |>-の字を数え上げ。
  MP T = - MP::one() / 3;
  FOR( i , 1 , 10 ){
    MP r = i == 7 ? A[0][i] - T : A[0][i]; // i == 7の時はnon-incuded C4で、11列目がうまく消える定数-1/3で帳尻を合わせる。
    FOR( j , i , 12 ){
      A[0][j] -= A[i][j] * r;
    }
    CERR( "i =" , i );
    CERR( A[0] );
    CERR( A[1] );
    CERR( A[2] );
    CERR( A[3] );
    CERR( A[4] );
    CERR( A[5] );
    CERR( A[6] );
    CERR( A[7] );
    CERR( A[8] );
    CERR( A[9] );
  }
  assert( A[0][7] == T );
  assert( A[0][10] == 0 );
  COUT( T );
  RETURN( A[0][11] );
}
REPEAT_MAIN(1);

#else /* INCLUDE_MAIN */
#ifdef INCLUDE_SUB

/* COMPAREに使用。圧縮時は削除する。*/
MP Naive( ll N , ll M , ll K , const bool& debug_output = true )
{
  MP answer{};
  return answer;
}

/* COMPAREに使用。圧縮時は削除する。*/
MP Answer( ll N , ll M , ll K , const bool& debug_output = true )
{
  MP answer{};
  return answer;
}

/* 圧縮時は中身だけ削除する。*/
IN VO Experiment()
{
  /* // 1変数 ../Contest/Template/Experiment/OneVariable.txt */
  /* // 2変数 ../Contest/Template/Experiment/TwoVariable.txt */
  /* // 3変数 ../Contest/Template/Experiment/ThreeVariable.txt */
  
}

/* 圧縮時は中身だけ削除する。*/
IN VO SmallTest()
{
  /* // 数 ../Contest/Template/SmallTest/Number.txt */
  /* // 配列 ../Contest/Template/SmallTest/Array.txt */
  /* // 順列 ../Contest/Template/SmallTest/Permutation.txt */
  /* // 文字列 ../Contest/Template/SmallTest/String.txt */
  /* // グリッド ../Contest/Template/SmallTest/Grid.txt */
  /* // グラフ ../Contest/Template/SmallTest/Graph.txt */
  /* // 重み付きグラフ ../Contest/Template/SmallTest/WeightedGraph.txt */
  /* // 区間クエリ ../Contest/Template/SmallTest/IntervalQuery.txt */
  
}

/* 圧縮時は中身だけ削除する。*/
IN VO RandomTest( const int& test_case_num )
{
  /* // 数 ../Contest/Template/SmallTest/Number.txt */
  /* // 配列 ../Contest/Template/SmallTest/Array.txt */
  /* // 順列 ../Contest/Template/SmallTest/Permutation.txt */
  /* // 文字列 ../Contest/Template/SmallTest/String.txt */
  /* // グリッド ../Contest/Template/SmallTest/Grid.txt */
  /* // グラフ ../Contest/Template/SmallTest/Graph.txt */
  /* // 重み付きグラフ ../Contest/Template/SmallTest/WeightedGraph.txt  */
  /* // 区間クエリ ../Contest/Template/SmallTest/IntervalQuery.txt  */
  /* // 多種クエリ ../Contest/Template/SmallTest/MultiTypeQuery.txt */
  REPEAT( test_case_num ){

  }  
}

#define INCLUDE_MAIN
#include __FILE__
#else /* INCLUDE_SUB */
#ifdef INCLUDE_LIBRARY

/* VVV 常設でないライブラリは以下に挿入する。*/
/* // Arithmetic ../Contest/Template/Library/Arithmetic.txt */
/* // BFS ../Contest/Template/Library/BFS.txt */
/* // BIT ../Contest/Template/Library/BIT.txt */
/* // CoordinateCompress ../Contest/Template/Library/CoordinateCompress.txt */
/* // DFS ../Contest/Template/Library/DFS.txt */
/* // DifferenceSequence ../Contest/Template/Library/DifferenceSequence.txt */
/* // Dijkstra ../Contest/Template/Library/Dijkstra.txt */
/* // Knapsack ../Contest/Template/Library/Knapsack.txt */
/* // Matrix ../Contest/Template/Library/Matrix.txt */
/* // Set ../Contest/Template/Library/Set.txt */
/* // Polynomial ../Contest/Template/Library/Polynomial.txt */
/* // SqrtDecomposition ../Contest/Template/Library/SqrtDecomposition.txt */
/* // UnionFind ../Contest/Template/Library/UnionFind.txt */

/* AAA 常設でないライブラリは以上に挿入する。*/

#define INCLUDE_SUB
#include __FILE__
#else /* INCLUDE_LIBRARY */
#ifdef DEBUG
  #define _GLIBCXX_DEBUG
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize ( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if CE( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
  #define FINISH_MAIN REPEAT( test_case_num ){ if CE( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
  #define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 )
  #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) )
  #ifdef USE_GETLINE
    #define SET_SEPARATE( SEPARATOR , ... ) VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
    #define SET( ... ) SET_SEPARATE( '\n' , __VA_ARGS__ )
    #define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; SET_SEPARATE( SEPARATOR , __VA_ARGS__ )
    #define GETLINE( ... ) GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
  #else
    #define SET( ... ) VariadicCin( cin , __VA_ARGS__ )
    #define CIN( LL , ... ) LL __VA_ARGS__; SET( __VA_ARGS__ )
    #define SET_A( I , N , ... ) VariadicResize( N + I , __VA_ARGS__ ); FOR( VARIABLE_FOR_SET_A , 0 , N ){ VariadicSet( cin , VARIABLE_FOR_SET_A + I , __VA_ARGS__ ); }
    #define CIN_A( LL , I , N , ... ) VE<LL> __VA_ARGS__; SET_A( I , N , __VA_ARGS__ )
    #define CIN_AA( LL , I0 , N0 , I1 , N1 , VAR ) VE<VE<LL>> VAR( N0 + I0 ); FOR( VARIABLE_FOR_CIN_AA , 0 , N0 ){ SET_A( I1 , N1 , VAR[VARIABLE_FOR_CIN_AA + I0] ); }
  #endif
  #define SET_ASSERT( A , MIN , MAX ) SET( A ); ASSERT( A , MIN , MAX )
  #define SOLVE_ONLY 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
  #define COUTNS( ... ) VariadicCoutNonSep( cout , __VA_ARGS__ )
  #define CERR( ... ) 
  #define CERRNS( ... ) 
  #define COUT_A( I , N , A ) CoutArray( cout , I , N , A ) << ENDL
  #define CERR_A( I , N , A ) 
#endif
#ifdef REACTIVE
  #ifdef DEBUG
    #define RSET( A , ... ) A = __VA_ARGS__
  #else
    #define RSET( A , ... ) SET( A )
  #endif
  #define RCIN( LL , A , ... ) LL A; RSET( A , __VA_ARGS__ )
  #define ENDL endl
#else
  #define ENDL "\n"
#endif
#include <bits/stdc++.h>
using namespace std;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now(); double loop_average_time = 0.0 , loop_start_time = 0.0 , current_time = 0.0; int loop_count = 0
#define CURRENT_TIME ( current_time = static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 ) )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME , loop_count == 0 ? loop_start_time = current_time : loop_average_time = ( current_time - loop_start_time ) / loop_count , ++loop_count , current_time < TL_MS - loop_average_time * 2 - 100.0 )
#define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE
#define SET_A_ASSERT( I , N , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A + I] , MIN , MAX ); }
#define SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_AA0 , 0 , N0 ){ FOR( VARIABLE_FOR_SET_AA1 , 0 , N1 ){ SET_ASSERT( A[VARIABLE_FOR_SET_AA0 + I0][VARIABLE_FOR_SET_AA1 + I1] , MIN , MAX ); } }
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A_ASSERT( I , N , A , MIN , MAX ) vector<decldecay_t( MAX )> A( N + I ); SET_A_ASSERT( I , N , A , MIN , MAX )
#define CIN_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) vector A( N0 + I0 , vector<decldecay_t( MAX )>( N1 + I1 ) ); SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( decldecay_t( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( decldecay_t( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( decldecay_t( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- )
#define ITR( ARRAY ) auto begin_ ## ARRAY = ARRAY .BE() , itr_ ## ARRAY = begin_ ## ARRAY , end_ ## ARRAY = ARRAY .EN()
#define FOR_ITR( ARRAY ) for( ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define RUN( ARRAY , ... ) for( auto&& __VA_ARGS__ : ARRAY )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS ); cerr << fixed << setprecision( DECIMAL_DIGITS )
#define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ , false ); auto answer = Answer( __VA_ARGS__ , false ); bool match = naive == answer; CERR( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; }

/* 圧縮用 */
#define TE template
#define TY typename
#define US using
#define ST static
#define AS assert
#define IN inline
#define CL class
#define PU public
#define OP operator
#define CE constexpr
#define CO const
#define NE noexcept
#define RE return 
#define WH while
#define VO void
#define VE vector
#define LI list
#define BE begin
#define EN end
#define SZ size
#define LE length
#define PW Power
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&
#define VI virtual 
#define IS basic_istream<char,Traits>
#define OS basic_ostream<char,Traits>
#define ST_AS static_assert
#define reMO_CO remove_const
#define is_COructible_v is_constructible_v
#define rBE rbegin

/* 型のエイリアス */
#define decldecay_t(VAR)decay_t<decltype(VAR)>
TE <TY F,TY...Args> US ret_t = decltype(declval<F>()(declval<Args>()...));
TE <TY T> US inner_t = TY T::type;
US uint = unsigned int;
US ll = long long;
US ull = unsigned long long;
US ld = long double;
US lld = __float128;
TE <TY INT> US T2 = pair<INT,INT>;
TE <TY INT> US T3 = tuple<INT,INT,INT>;
TE <TY INT> US T4 = tuple<INT,INT,INT,INT>;
US path = pair<int,ll>;

/* VVV 常設ライブラリは以下に挿入する。*/
#ifdef DEBUG
  #include "C:/Users/user/Documents/Programming/Contest/Template/Local/a_Body.hpp"
#else
/* BinarySearch (2KB)*/
/* EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CONST_TARGETの整数解を格納。*/
#define BS(AN,MINIMUM,MAXIMUM,EXPRESSION,DESIRED_INEQUALITY,CO_TARGET,INEQUALITY_FOR_CHECK,UPDATE_U,UPDATE_L,UPDATE_AN)ST_AS(! is_same<decldecay_t(CO_TARGET),uint>::value && ! is_same<decldecay_t(CO_TARGET),ull>::value);ll AN = MINIMUM;{ll AN ## _L = MINIMUM;ll AN ## _R = MAXIMUM;AN = UPDATE_AN;ll EXPRESSION_BS;CO ll CO_TARGET_BS =(CO_TARGET);ll DIFFERENCE_BS;WH(AN ## _L < AN ## _R){DIFFERENCE_BS =(EXPRESSION_BS =(EXPRESSION))- CO_TARGET_BS;if(DIFFERENCE_BS INEQUALITY_FOR_CHECK 0){AN ## _R = UPDATE_U;}else{AN ## _L = UPDATE_L;}AN = UPDATE_AN;}if(AN ## _L > AN ## _R || !((EXPRESSION)DESIRED_INEQUALITY CO_TARGET_BS)){AN = MAXIMUM + 1;}}
/* 単調増加の時にEXPRESSION >= CONST_TARGETの最小解を格納。*/
#define BS1(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,>=,CO_TARGET,>=,AN,AN + 1,(AN ## _L + AN ## _R)/ 2)
/* 単調増加の時にEXPRESSION <= CONST_TARGETの最大解を格納。*/
#define BS2(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,<=,CO_TARGET,>,AN - 1,AN,(AN ## _L + 1 + AN ## _R)/ 2)
/* 単調減少の時にEXPRESSION >= CONST_TARGETの最大解を格納。*/
#define BS3(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,>=,CO_TARGET,<,AN - 1,AN,(AN ## _L + 1 + AN ## _R)/ 2)
/* 単調減少の時にEXPRESSION <= CONST_TARGETの最小解を格納。*/
#define BS4(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,<=,CO_TARGET,<=,AN,AN + 1,(AN ## _L + AN ## _R)/ 2)

/* TwoPoitnterApproach (2KB)*/
/* VAR_TPAは尺取り法用の変数名の接頭辞で、実際の変数名ではなく、_Lと_Rと_infoがつく。
ANSWER ## _temp = {VAR_TPA ## _L,VAR_TPA ## _R,VPA_TPA ## _info}を
{INIT,INIT,INFO_init}で初期化する。VPA_TPA ## _infoは区間和など。
ANSWER ## _tempがCONTINUE_CONDITIONを満たす限り、ANSWER ## _tempが
条件ON_CONDITIONを満たすか否かを判定し、それがtrueになるか
VAR_TAR ## _LがVAR_TAR ## _Rに追い付くまでVAR_TPA ## _LとVPA_TPA ## _infoの
更新操作UPDATE_Lを繰り返し、その後VAR_TPA ## _RとVPA_TPA ## _infoの
更新操作UPDATE_Rを行う。（マクロとコンマの制約上、関数オブジェクトを用いる）
ON_CONDITIONがtrueとなる極大閉区間とその時点でのinfoをANSWERに格納する。
例えば長さNの非負整数値配列Aで極大な正値区間とそこでの総和を取得したい場合
auto update_L = [&]( int& i_L , auto& i_info ){ i_info -= A[i_L++]; };
auto update_R = [&]( int& i_R , auto& i_info ){ if( ++i_R < N ){ i_info += A[i_R]; } };
TPA( interval , i , 0 , i_R < N , update_L( i_L , i_info ) , update_R( i_R , i_info ) , A[i_L] > 0 && A[i_R] > 0 , ll( A[0] ) );
とすればtuple<int,int,ll>値配列intervalに{左端,右端,総和}の列が格納される。
VAR_TPA ## _infoもintervalにコピーされるので、setやvectorなどのコピーのコストが
大きいデータを用いてon,off判定する時はTPAより前に宣言して使う。*/
#define TPA(AN,VAR_TPA,INIT,CONTINUE_CONDITION,UPDATE_L,UPDATE_R,ON_CONDITION,INFO_init)VE<tuple<decldecay_t(INIT),decldecay_t(INIT),decldecay_t(INFO_init)>> AN{};{auto init_TPA = INIT;decldecay_t(AN.front())AN ## _temp ={init_TPA,init_TPA,INFO_init};auto AN ## _prev = AN ## _temp;auto& VAR_TPA ## _L = get<0>(AN ## _temp);auto& VAR_TPA ## _R = get<1>(AN ## _temp);auto& VAR_TPA ## _info = get<2>(AN ## _temp);bool on_TPA_prev = false;WH(true){bool continuing = CONTINUE_CONDITION;bool on_TPA = continuing &&(ON_CONDITION);if(on_TPA_prev && ! on_TPA){AN.push_back(AN ## _prev);}if(continuing){if(on_TPA || VAR_TPA ## _L == VAR_TPA ## _R){AN ## _prev = AN ## _temp;UPDATE_R;}else{UPDATE_L;}}else{break;}on_TPA_prev = on_TPA;}}

/* Random (1KB)*/
ll GetRand(CRI Rand_min,CRI Rand_max){AS(Rand_min <= Rand_max);ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;}

/* Set (1KB)*/
#define DC_OF_HASH(...)struct hash<__VA_ARGS__>{IN size_t OP()(CO __VA_ARGS__& n)CO;};
CL is_ordered{PU:is_ordered()= delete;TE <TY T> ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE <TY T> ST CE CO bool value = is_same_v< decltype(Check(declval<T>())),true_type >;};
TE <TY T>US Set = conditional_t<is_COructible_v<unordered_set<T>>,unordered_set<T>,conditional_t<is_ordered::value<T>,set<T>,VO>>;

/* Tuple (5KB)*/
#define DF_OF_AR_FOR_TUPLE(OPR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP OPR ## =(V<T,U>& t0,CO V<T,U>& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);RE t0;}TE <TY T,TY U,TY V> IN tuple<T,U,V>& OP OPR ## =(tuple<T,U,V>& t0,CO tuple<T,U,V>& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);RE t0;}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP OPR ## =(tuple<T,U,V,W>& t0,CO tuple<T,U,V,W>& t1){get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);get<2>(t0)OPR ## = get<2>(t1);get<3>(t0)OPR ## = get<3>(t1);RE t0;}TE <TY ARG,TY T,TY U,TE <TY...> TY V> IN auto OP OPR ## =(V<T,U>& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;RE t0;}TE <TY ARG,TY T,TY U,TY V> IN tuple<T,U,V>& OP OPR ## =(tuple<T,U,V>& t0,CO ARG& t1){get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;RE t0;}TE <TY ARG,TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP OPR ## =(tuple<T,U,V,W>& t0,CO ARG& t1){get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;get<3>(t0)OPR ## = t1;RE t0;}TE <TE <TY...> TY V,TY...ARGS,TY ARG> IN auto OP OPR(CO V<ARGS...>& t0,CO ARG& t1)-> decldecay_t((get<0>(t0),t0)){auto t = t0;RE MO(t OPR ## = t1);}
#define DF_OF_INCREMENT_FOR_TUPLE(INCR)TE <TY T,TY U,TE <TY...> TY V> IN auto OP INCR(V<T,U>& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);RE t;}TE <TY T,TY U,TY V> IN tuple<T,U,V>& OP INCR(tuple<T,U,V>& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);RE t;}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W>& OP INCR(tuple<T,U,V,W>& t){INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);INCR get<3>(t);RE t;}
TE <CL Traits,TY T> IN IS& OP>>(IS& is,tuple<T>& arg){RE is >> get<0>(arg);}TE <CL Traits,TY T,TY U,TE <TY...> TY V> IN auto OP>>(IS& is,V<T,U>& arg)-> decltype((get<0>(arg),is))&{RE is >> get<0>(arg)>> get<1>(arg);}TE <CL Traits,TY T,TY U,TY V> IN IS& OP>>(IS& is,tuple<T,U,V>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg);}TE <CL Traits,TY T,TY U,TY V,TY W> IN IS& OP>>(IS& is,tuple<T,U,V,W>& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg)>> get<3>(arg);}TE <CL Traits,TY T> IN OS& OP<<(OS& os,CO tuple<T>& arg){RE os << get<0>(arg);}TE <CL Traits,TY T,TY U,TE <TY...> TY V> IN auto OP<<(OS& os,CO V<T,U>& arg)-> decltype((get<0>(arg),os))&{RE os << get<0>(arg)<< " " << get<1>(arg);}TE <CL Traits,TY T,TY U,TY V> IN OS& OP<<(OS& os,CO tuple<T,U,V>& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg);}TE <CL Traits,TY T,TY U,TY V,TY W> IN OS& OP<<(OS& os,CO tuple<T,U,V,W>& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg)<< " " << get<3>(arg);}DF_OF_AR_FOR_TUPLE(+);TE <TY T,TY U,TE <TY...> TY V> IN auto OP-(CO V<T,U>& t)-> decltype(get<0>(t),t){RE{-get<0>(t),-get<1>(t)};}TE <TY T,TY U,TY V> IN tuple<T,U,V> OP-(CO tuple<T,U,V>& t){RE{-get<0>(t),-get<1>(t),-get<2>(t)};}TE <TY T,TY U,TY V,TY W> IN tuple<T,U,V,W> OP-(CO tuple<T,U,V,W>& t){RE{-get<0>(t),-get<1>(t),-get<2>(t),-get<3>(t)};}DF_OF_AR_FOR_TUPLE(-);DF_OF_AR_FOR_TUPLE(*);DF_OF_AR_FOR_TUPLE(/);DF_OF_AR_FOR_TUPLE(%);DF_OF_INCREMENT_FOR_TUPLE(++);DF_OF_INCREMENT_FOR_TUPLE(--);

#define DF_OF_HASH_FOR_TUPLE(PAIR)TE <TY T,TY U> IN size_t hash<PAIR<T,U>>::OP()(CO PAIR<T,U>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<T> h0;ST CO hash<U> h1;RE(h0(get<0>(n))* seed)^ h1(get<1>(n));}
TE <TY T> DC_OF_HASH(tuple<T>);TE <TY T,TY U> DC_OF_HASH(pair<T,U>);TE <TY T,TY U> DC_OF_HASH(tuple<T,U>);TE <TY T,TY U,TY V> DC_OF_HASH(tuple<T,U,V>);TE <TY T,TY U,TY V,TY W> DC_OF_HASH(tuple<T,U,V,W>);
TE <TY T> IN size_t hash<tuple<T>>::OP()(CO tuple<T>& n)CO{ST CO hash<T> h;RE h(get<0>(n));}DF_OF_HASH_FOR_TUPLE(pair);DF_OF_HASH_FOR_TUPLE(tuple);TE <TY T,TY U,TY V> IN size_t hash<tuple<T,U,V>>::OP()(CO tuple<T,U,V>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<pair<T,U>> h01;ST CO hash<V> h2;RE(h01({get<0>(n),get<1>(n)})* seed)^ h2(get<2>(n));}TE <TY T,TY U,TY V,TY W> IN size_t hash<tuple<T,U,V,W>>::OP()(CO tuple<T,U,V,W>& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash<pair<T,U>> h01;ST CO hash<pair<V,W>> h23;RE(h01({get<0>(n),get<1>(n)})* seed)^ h23({get<2>(n),get<3>(n)});}

/* Vector (2KB)*/
#define DF_OF_COUT_FOR_VE(V)TE <CL Traits,TY Arg> IN OS& OP<<(OS& os,CO V<Arg>& arg){auto BE = arg.BE(),EN = arg.EN();auto IT = BE;WH(IT != EN){(IT == BE?os:os << " ")<< *IT;IT++;}RE os;}
#define DF_OF_AR_FOR_VE(V,OPR)TE <TY T> IN V<T>& OP OPR ## =(V<T>& a,CO T& t){for(auto& s:a){s OPR ## = t;}RE a;}TE <TY T> IN V<T>& OP OPR ## =(V<T>& a0,CO V<T>& a1){AS(a0.SZ()<= a1.SZ());auto IT0 = a0.BE(),EN0 = a0.EN();auto IT1 = a1.BE();WH(IT0 != EN0){*(IT0++)OPR ## = *(IT1++);}RE a0;}TE <TY T,TY U> IN V<T> OP OPR(V<T> a,CO U& u){RE MO(a OPR ## = u);}
#define DF_OF_INCREMENT_FOR_VE(V,INCR)TE <TY T> IN V<T>& OP INCR(V<T>& a){for(auto& i:a){INCR i;}RE a;}
#define DF_OF_ARS_FOR_VE(V)DF_OF_AR_FOR_VE(V,+);DF_OF_AR_FOR_VE(V,-);DF_OF_AR_FOR_VE(V,*);DF_OF_AR_FOR_VE(V,/);DF_OF_AR_FOR_VE(V,%);DF_OF_INCREMENT_FOR_VE(V,++);DF_OF_INCREMENT_FOR_VE(V,--);TE <TY T> IN V<T> OP*(CO T& scalar,V<T> v){for(auto& t:v){t *= scalar;}RE MO(v);}
DF_OF_COUT_FOR_VE(VE);DF_OF_COUT_FOR_VE(LI);DF_OF_ARS_FOR_VE(VE);DF_OF_ARS_FOR_VE(LI);IN VO VariadicResize(CRI SZ){}TE <TY Arg,TY... ARGS> IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.resize(SZ);VariadicResize(SZ,args...);}TE <TY V> IN auto Get(V& a){RE[&](CRI i = 0)-> CO decldecay_t(a[0])&{RE a[i];};}TE <TY T = int> IN VE<T> id(CRI SZ){VE<T> AN(SZ);FOR(i,0,SZ){AN[i]= i;}RE AN;}TE <TY T> VO Sort(VE<T>& a,CO bool& reversed = false){if(reversed){ST auto comp =[](CO T& t0,CO T& t1){RE t1 < t0;};sort(a.BE(),a.EN(),comp);}else{sort(a.BE(),a.EN());}}TE <TY T> IN VE<int> IndexSort(CO VE<T>& a,CO bool& reversed = false){auto index = id<int>(a.SZ());if(reversed){sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE a[j]< a[i];});}else{sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE a[i]< a[j];});}RE index;}TE <TY T,TY U = T> IN U Sum(CO VE<T>& a){U AN{};for(auto& x:a){AN += x;}RE AN;}TE <TY T,TY U = T> IN U Product(CO VE<T>& a){U AN{};for(auto& x:a){AN *= x;}RE AN;}

/* Map (1KB)*/
#define DF_OF_AR_FOR_MAP(MAP,OPR)TE <TY T,TY U> IN MAP<T,U>& OP OPR ## =(MAP<T,U>& a,CO pair<T,U>& v){a[v.first]OPR ## = v.second;RE a;}TE <TY T,TY U> IN MAP<T,U>& OP OPR ## =(MAP<T,U>& a0,CO MAP<T,U>& a1){for(auto&[t,u]:a1){a0[t]OPR ## = u;}RE a0;}TE <TY T,TY U,TY ARG> IN MAP<T,U> OP OPR(MAP<T,U> a,CO ARG& arg){RE MO(a OPR ## = arg);}
#define DF_OF_ARS_FOR_MAP(MAP)DF_OF_AR_FOR_MAP(MAP,+);DF_OF_AR_FOR_MAP(MAP,-);DF_OF_AR_FOR_MAP(MAP,*);DF_OF_AR_FOR_MAP(MAP,/);DF_OF_AR_FOR_MAP(MAP,%);
TE <TY T,TY U>US Map = conditional_t<is_COructible_v<unordered_map<T,int>>,unordered_map<T,U>,conditional_t<is_ordered::value<T>,map<T,U>,VO>>;
DF_OF_ARS_FOR_MAP(map);DF_OF_ARS_FOR_MAP(unordered_map);

/* StdStream (2KB)*/
TE <CL Traits> IN IS& VariadicCin(IS& is){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicCin(IS& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);}TE <CL Traits> IN IS& VariadicSet(IS& is,CRI i){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicSet(IS& is,CRI i,Arg& arg,ARGS&... args){RE VariadicSet(is >> arg[i],i,args...);}TE <CL Traits> IN IS& VariadicGetline(IS& is,CO char& separator){RE is;}TE <CL Traits,TY Arg,TY... ARGS> IN IS& VariadicGetline(IS& is,CO char& separator,Arg& arg,ARGS&... args){RE VariadicGetline(getline(is,arg,separator),separator,args...);}TE <CL Traits,TY Arg> IN OS& VariadicCout(OS& os,Arg&& arg){RE os << forward<Arg>(arg);}TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN OS& VariadicCout(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCout(os << forward<Arg1>(arg1)<< " ",forward<Arg2>(arg2),forward<ARGS>(args)...);}TE <CL Traits,TY Arg> IN OS& VariadicCoutNonSep(OS& os,Arg&& arg){RE os << forward<Arg>(arg);}TE <CL Traits,TY Arg1,TY Arg2,TY... ARGS> IN OS& VariadicCoutNonSep(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCoutNonSep(os << forward<Arg1>(arg1),forward<Arg2>(arg2),forward<ARGS>(args)...);}TE <CL Traits,TY ARRAY> IN OS& CoutArray(OS& os,CRI i_start,CRI i_ulim,ARRAY&& a){for(int i = i_start;i < i_ulim;i++){(i == i_start?os:(os << " "))<< a[i];}RE os;}

/* Module (6KB)*/
#define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE
#define DC_OF_POINT(POINT)IN U& POINT()NE
#define DF_OF_CPOINT(POINT)TE <TY U> IN CO U& VirtualPointedSet<U>::POINT()CO NE{RE Point();}
#define DF_OF_POINT(POINT)TE <TY U> IN U& VirtualPointedSet<U>::POINT()NE{RE Point();}
TE <TY U>CL UnderlyingSet{PU:US type = U;};TE <TY U>CL VirtualPointedSet:VI PU UnderlyingSet<U>{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE <TY U>CL PointedSet:VI PU VirtualPointedSet<U>{PU:U m_b_U;IN PointedSet(U b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE <TY U>CL VirtualNSet:VI PU UnderlyingSet<U>{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE <TY U,TY F_U>CL AbstractNSet:VI PU VirtualNSet<U>{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN AbstractNSet<U,F_U>& OP=(CO AbstractNSet&)NE;IN U Transfer(CO U& u);};TE <TY U>CL VirtualMagma:VI PU UnderlyingSet<U>{PU:VI U Product(U u0,CO U& u1)= 0;IN U Sum(U u0,CO U& u1);};TE <TY U = ll>CL AdditiveMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U = ll>CL MultiplicativeMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U,TY M_U>CL AbstractMagma:VI PU VirtualMagma<U>{PU:M_U m_m_U;IN AbstractMagma(M_U m_U);IN AbstractMagma<U,M_U>& OP=(CO AbstractMagma<U,M_U>&)NE;IN U Product(U u0,CO U& u1);};
TE <TY U> IN PointedSet<U>::PointedSet(U b_U):m_b_U(MO(b_U)){}TE <TY U> IN CO U& PointedSet<U>::Point()CO NE{RE m_b_U;}TE <TY U> IN U& PointedSet<U>::Point()NE{RE m_b_U;}DF_OF_CPOINT(Unit);DF_OF_CPOINT(Zero);DF_OF_CPOINT(One);DF_OF_CPOINT(Infty);DF_OF_POINT(init);DF_OF_POINT(root);TE <TY U,TY F_U> IN AbstractNSet<U,F_U>::AbstractNSet(F_U f_U):m_f_U(MO(f_U)){ST_AS(is_invocable_r_v<U,F_U,U>);}TE <TY U,TY F_U> IN AbstractNSet<U,F_U>& AbstractNSet<U,F_U>::operator=(CO AbstractNSet<U,F_U>&)NE{RE *TH;}TE <TY U,TY F_U> IN U AbstractNSet<U,F_U>::Transfer(CO U& u){RE m_f_U(u);}TE <TY U> IN U VirtualNSet<U>::Inverse(CO U& u){RE Transfer(u);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>::AbstractMagma(M_U m_U):m_m_U(MO(m_U)){ST_AS(is_invocable_r_v<U,M_U,U,U>);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>& AbstractMagma<U,M_U>::OP=(CO AbstractMagma<U,M_U>&)NE{RE *TH;}TE <TY U> IN U AdditiveMagma<U>::Product(U u0,CO U& u1){RE MO(u0 += u1);}TE <TY U> IN U MultiplicativeMagma<U>::Product(U u0,CO U& u1){RE MO(u0 *= u1);}TE <TY U,TY M_U> IN U AbstractMagma<U,M_U>::Product(U u0,CO U& u1){RE m_m_U(MO(u0),u1);}TE <TY U> IN U VirtualMagma<U>::Sum(U u0,CO U& u1){RE Product(MO(u0),u1);}

TE <TY U>CL VirtualMonoid:VI PU VirtualMagma<U>,VI PU VirtualPointedSet<U>{};TE <TY U = ll>CL AdditiveMonoid:VI PU VirtualMonoid<U>,PU AdditiveMagma<U>,PU PointedSet<U>{};TE <TY U = ll>CL MultiplicativeMonoid:VI PU VirtualMonoid<U>,PU MultiplicativeMagma<U>,PU PointedSet<U>{PU:IN MultiplicativeMonoid(U e_U);};TE <TY U,TY M_U>CL AbstractMonoid:VI PU VirtualMonoid<U>,PU AbstractMagma<U,M_U>,PU PointedSet<U>{PU:IN AbstractMonoid(M_U m_U,U e_U);};
TE <TY U> IN MultiplicativeMonoid<U>::MultiplicativeMonoid(U e_U):PointedSet<U>(MO(e_U)){}TE <TY U,TY M_U> IN AbstractMonoid<U,M_U>::AbstractMonoid(M_U m_U,U e_U):AbstractMagma<U,M_U>(MO(m_U)),PointedSet<U>(MO(e_U)){}

TE <TY U>CL VirtualGroup:VI PU VirtualMonoid<U>,VI PU VirtualPointedSet<U>,VI PU VirtualNSet<U>{};TE <TY U = ll>CL AdditiveGroup:VI PU VirtualGroup<U>,PU AdditiveMonoid<U>{PU:IN U Transfer(CO U& u);};TE <TY U,TY M_U,TY I_U>CL AbstractGroup:VI PU VirtualGroup<U>,PU AbstractMonoid<U,M_U>,PU AbstractNSet<U,I_U>{PU:IN AbstractGroup(M_U m_U,U e_U,I_U i_U);};
TE <TY U,TY M_U,TY I_U> IN AbstractGroup<U,M_U,I_U>::AbstractGroup(M_U m_U,U e_U,I_U i_U):AbstractMonoid<U,M_U>(MO(m_U),MO(e_U)),AbstractNSet<U,I_U>(MO(i_U)){}TE <TY U> IN U AdditiveGroup<U>::Transfer(CO U& u){RE -u;}

TE <TY R,TY U>CL VirtualRSet:VI PU UnderlyingSet<U>{PU:VI U Action(CO R& r,U u)= 0;IN U PW(U u,CO R& r);IN U ScalarProduct(CO R& r,U u);};TE <TY U,TY MAGMA>CL RegularRSet:VI PU VirtualRSet<U,U>,PU MAGMA{PU:IN RegularRSet(MAGMA magma);IN U Action(CO U& r,U u);};TE <TY MAGMA> RegularRSet(MAGMA magma)-> RegularRSet<inner_t<MAGMA>,MAGMA>;TE <TY R,TY U,TY O_U>CL AbstractRSet:VI PU VirtualRSet<R,U>{PU:O_U m_o_U;IN AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U);IN AbstractRSet<R,U,O_U>& OP=(CO AbstractRSet<R,U,O_U>&)NE;IN U Action(CO R& r,U u);};TE <TY R,TY U,TY O_U,TY GROUP>CL AbstractModule:PU AbstractRSet<R,U,O_U>,PU GROUP{PU:IN AbstractModule(CO R& dummy,O_U o_U,GROUP M);};TE <TY R,TY O_U,TY GROUP> AbstractModule(CO R& dummy,O_U o_U,GROUP M)-> AbstractModule<R,inner_t<GROUP>,O_U,GROUP>;TE <TY R,TY U>CL Module:VI PU VirtualRSet<R,U>,PU AdditiveGroup<U>{PU:IN U Action(CO R& r,U u);};
TE <TY R,TY MAGMA> IN RegularRSet<R,MAGMA>::RegularRSet(MAGMA magma):MAGMA(MO(magma)){}TE <TY R,TY U,TY O_U> IN AbstractRSet<R,U,O_U>::AbstractRSet(CO R& dummy0,CO U& dummy1,O_U o_U):m_o_U(MO(o_U)){ST_AS(is_invocable_r_v<U,O_U,R,U>);}TE <TY R,TY U,TY O_U,TY GROUP> IN AbstractModule<R,U,O_U,GROUP>::AbstractModule(CO R& dummy,O_U o_U,GROUP M):AbstractRSet<R,U,O_U>(dummy,M.One(),MO(o_U)),GROUP(MO(M)){ST_AS(is_same_v<U,inner_t<GROUP>>);}TE <TY R,TY U,TY O_U> IN AbstractRSet<R,U,O_U>& AbstractRSet<R,U,O_U>::OP=(CO AbstractRSet<R,U,O_U>&)NE{RE *TH;}TE <TY U,TY MAGMA> IN U RegularRSet<U,MAGMA>::Action(CO U& r,U u){RE TH->Product(r,MO(u));}TE <TY R,TY U,TY O_U> IN U AbstractRSet<R,U,O_U>::Action(CO R& r,U u){RE m_o_U(r,MO(u));}TE <TY R,TY U> IN U Module<R,U>::Action(CO R& r,U u){RE MO(u *= r);}TE <TY R,TY U> IN U VirtualRSet<R,U>::PW(U u,CO R& r){RE Action(r,MO(u));}TE <TY R,TY U> IN U VirtualRSet<R,U>::ScalarProduct(CO R& r,U u){RE Action(r,MO(u));}

/* Graph (5KB)*/
TE <TY T,TY R1,TY R2,TY E>CL VirtualGraph:VI PU UnderlyingSet<T>{PU:VI R1 Enumeration(CRI i)= 0;IN R2 Enumeration_inv(CO T& t);TE <TY PATH> IN R2 Enumeration_inv(CO PATH& p);IN VO Reset();VI CRI SZ()CO NE = 0;VI E& edge()NE = 0;VI ret_t<E,T> Edge(CO T& t)= 0;TE <TY PATH> IN ret_t<E,T> Edge(CO PATH& p);ST IN CO T& Vertex(CO T& t)NE;TE <TY PATH> ST IN CO T& Vertex(CO PATH& e)NE;VI R2 Enumeration_inv_Body(CO T& t)= 0;};TE <TY T,TY R1,TY R2,TY E>CL EdgeImplimentation:VI PU VirtualGraph<T,R1,R2,E>{PU:int m_SZ;E m_edge;IN EdgeImplimentation(CRI SZ,E edge);IN CRI SZ()CO NE;IN E& edge()NE;IN ret_t<E,T> Edge(CO T& t);};TE <TY E>CL Graph:PU EdgeImplimentation<int,CRI,CRI,E>{PU:IN Graph(CRI SZ,E edge);IN CRI Enumeration(CRI i);TE <TY F> IN Graph<F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CRI t);};TE <TY T,TY Enum_T,TY Enum_T_inv,TY E>CL EnumerationGraph:PU EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>{PU:Enum_T m_enum_T;Enum_T_inv m_enum_T_inv;IN EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge);IN ret_t<Enum_T,int> Enumeration(CRI i);TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> GetGraph(F edge)CO;IN ret_t<Enum_T_inv,T> Enumeration_inv_Body(CO T& t);};TE <TY Enum_T,TY Enum_T_inv,TY E> EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge)-> EnumerationGraph<decldecay_t(declval<Enum_T>()(0)),Enum_T,Enum_T_inv,E>;TE <TY T,TY E>CL MemorisationGraph:PU EdgeImplimentation<T,T,CRI,E>{PU:int m_LE;VE<T> m_memory;Map<T,int> m_memory_inv;IN MemorisationGraph(CRI SZ,CO T& dummy,E edge);IN T Enumeration(CRI i);IN VO Reset();TE <TY F> IN MemorisationGraph<T,F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CO T& t);};
TE <TY T,TY R1,TY R2,TY E> IN EdgeImplimentation<T,R1,R2,E>::EdgeImplimentation(CRI SZ,E edge):m_SZ(SZ),m_edge(MO(edge)){ST_AS(is_COructible_v<T,R1> && is_COructible_v<int,R2> && is_invocable_v<E,T>);}TE <TY E> IN Graph<E>::Graph(CRI SZ,E edge):EdgeImplimentation<int,CRI,CRI,E>(SZ,MO(edge)){}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN EnumerationGraph<T,Enum_T,Enum_T_inv,E>::EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge):EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>(SZ,MO(edge)),m_enum_T(MO(enum_T)),m_enum_T_inv(MO(enum_T_inv)){}TE <TY T,TY E> IN MemorisationGraph<T,E>::MemorisationGraph(CRI SZ,CO T& dummy,E edge):EdgeImplimentation<T,T,CRI,E>(SZ,MO(edge)),m_LE(),m_memory(),m_memory_inv(){ST_AS(is_invocable_v<E,T>);}TE <TY E> IN CRI Graph<E>::Enumeration(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T,int> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration(CRI i){RE m_enum_T(i);}TE <TY T,TY E> IN T MemorisationGraph<T,E>::Enumeration(CRI i){AS(0 <= i && i < m_LE);RE m_memory[i];}TE <TY T,TY R1,TY R2,TY E> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO T& t){RE Enumeration_inv_Body(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO PATH& p){RE Enumeration_inv_Body(get<0>(p));}TE <TY E> IN CRI Graph<E>::Enumeration_inv_Body(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T_inv,T> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration_inv_Body(CO T& t){RE m_enum_T_inv(t);}TE <TY T,TY E> IN CRI MemorisationGraph<T,E>::Enumeration_inv_Body(CO T& t){if(m_memory_inv.count(t)== 0){AS(m_LE < TH->SZ());m_memory.push_back(t);RE m_memory_inv[t]= m_LE++;}RE m_memory_inv[t];}TE <TY T,TY R1,TY R2,TY E> VO VirtualGraph<T,R1,R2,E>::Reset(){}TE <TY T,TY E> IN VO MemorisationGraph<T,E>::Reset(){m_LE = 0;m_memory.clear();m_memory_inv.clear();}TE <TY T,TY R1,TY R2,TY E> IN CRI EdgeImplimentation<T,R1,R2,E>::SZ()CO NE{RE m_SZ;}TE <TY T,TY R1,TY R2,TY E> IN E& EdgeImplimentation<T,R1,R2,E>::edge()NE{RE m_edge;}TE <TY T,TY R1,TY R2,TY E> IN ret_t<E,T> EdgeImplimentation<T,R1,R2,E>::Edge(CO T& t){RE m_edge(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN ret_t<E,T> VirtualGraph<T,R1,R2,E>::Edge(CO PATH& p){RE Edge(get<0>(p));}TE <TY E> TE <TY F> IN Graph<F> Graph<E>::GetGraph(F edge)CO{RE Graph<F>(TH->SZ(),MO(edge));}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::GetGraph(F edge)CO{RE EnumerationGraph<T,Enum_T,Enum_T_inv,F>(TH->SZ(),m_enum_T,m_enum_T_inv,MO(edge));}TE <TY T,TY E> TE <TY F> IN MemorisationGraph<T,F> MemorisationGraph<T,E>::GetGraph(F edge)CO{RE MemorisationGraph<T,F>(TH->SZ(),MO(edge));}TE <TY T,TY R1,TY R2,TY E> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO T& t)NE{RE t;}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO PATH& e)NE{RE Vertex(get<0>(e));}

/* Grid (2KB)*/
#define SET_GRID H_minus = H - 1;W_minus = W - 1;HW = ll(H)* W
#define SET_HW(h,w)H = h;W = w;SET_GRID
#define CIN_HW SET(H,W);SET_GRID
TE <TY E>CL GridGraph:PU EnumerationGraph<T2<int>,T2<int>(&)(CRI),int(&)(CO T2<int>&),E>{PU:IN GridGraph(E e);};int H,W,H_minus,W_minus;ll HW;VE<string> grid;char walkable = '.',unwalkable = '#';
IN T2<int> EnumHW(CRI v){RE{v / W,v % W};}IN int EnumHW_inv(CO T2<int>& ij){auto&[i,j]= ij;RE i * W + j;}TE <TY E> IN GridGraph<E>::GridGraph(E e):EnumerationGraph<T2<int>,T2<int>(&)(CRI),int(&)(CO T2<int>&),E>(HW,EnumHW,EnumHW_inv,MO(e)){AS(HW >> 31 == 0 && H * W == HW);}VE<T2<int>> EdgeOnGrid(CO T2<int>& v){VE<T2<int>> AN{};auto&[i,j]= v;if(grid[i][j]== walkable){if(i > 0 && grid[i-1][j]== walkable){AN.push_back({i-1,j});}if(i+1 < H && grid[i+1][j]== walkable){AN.push_back({i+1,j});}if(j > 0 && grid[i][j-1]== walkable){AN.push_back({i,j-1});}if(j+1 < W && grid[i][j+1]== walkable){AN.push_back({i,j+1});}}RE AN;}VE<pair<T2<int>,ll>> WEdgeOnGrid(CO T2<int>& v){VE<pair<T2<int>,ll>> AN{};auto&[i,j]= v;if(grid[i][j]== walkable){if(i>0 && grid[i-1][j]== walkable){AN.push_back({{i-1,j},1});}if(i+1 < H && grid[i+1][j]== walkable){AN.push_back({{i+1,j},1});}if(j>0 && grid[i][j-1]== walkable){AN.push_back({{i,j-1},1});}if(j+1 < W && grid[i][j+1]== walkable){AN.push_back({{i,j+1},1});}}RE AN;}IN VO SetWallStringOnGrid(){grid.resize(H);for(int i = 0;i < H;i++){SET(grid[i]);AS(int(grid[i].SZ())== W);}}CO string direction="URDL";IN int DirectionNumberOnGrid(CRI i,CRI j,CRI k,CRI h){RE i < k?2:i > k?0:j < h?1:(AS(j > h),3);}IN int DirectionNumberOnGrid(CO T2<int>& v,CO T2<int>& w){auto&[i,j]= v;auto&[k,h]= w;RE DirectionNumberOnGrid(i,j,k,h);}IN int DirectionNumberOnGrid(CRI v,CRI w){RE DirectionNumberOnGrid(EnumHW(v),EnumHW(w));}IN int ReverseDirectionNumberOnGrid(CRI n){AS(0 <= n && n<4);RE n ^ 2;}

/* ConstexprModulo (7KB)*/
CEXPR(uint,P,998244353);
#define RP Represent
#define DeRP Derepresent

TE <uint M,TY INT> CE INT Residue(INT n)NE{RE MO(n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n < INT(M)?n:n %= M);}TE <TY INT> CE INT& ResidueP(INT& n)NE{CE CO uint trunc =(1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq =(n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}
TE <uint M> CL Mod;TE <uint M>CL COantsForMod{PU:COantsForMod()= delete;ST CE CO uint g_memory_bound = 1e6;ST CE CO uint g_memory_LE = M < g_memory_bound?M:g_memory_bound;ST CE uint g_M_minus = M - 1;ST CE int g_order_minus_1 = M - 2;ST CE int g_order_minus_1_neg = -g_order_minus_1;};
#define SFINAE_FOR_MOD enable_if_t<is_COructible_v<uint,decay_t<T>>>*
#define DC_OF_CM_FOR_MOD(OPR)CE bool OP OPR(CO Mod<M>& n)CO NE
#define DC_OF_AR_FOR_MOD(OPR,EX)CE Mod<M> OP OPR(Mod<M> n)CO EX;
#define DF_OF_CM_FOR_MOD(OPR)TE <uint M> CE bool Mod<M>::OP OPR(CO Mod<M>& n)CO NE{RE m_n OPR n.m_n;}
#define DF_OF_AR_FOR_MOD(OPR,EX,LEFT,OPR2)TE <uint M> CE Mod<M> Mod<M>::OP OPR(Mod<M> n)CO EX{RE MO(LEFT OPR2 ## = *TH);}TE <uint M,TY T,SFINAE_FOR_MOD = nullptr> CE Mod<M> OP OPR(T n0,CO Mod<M>& n1)EX{RE MO(Mod<M>(MO(n0))OPR ## = n1);}
TE <uint M>CL Mod{PU:uint m_n;CE Mod()NE;CE Mod(CO Mod<M>& n)NE;CE Mod(Mod<M>&& n)NE;TE <TY T,SFINAE_FOR_MOD = nullptr> CE Mod(T n)NE;CE Mod<M>& OP=(Mod<M> n)NE;CE Mod<M>& OP+=(CO Mod<M>& n)NE;CE Mod<M>& OP-=(CO Mod<M>& n)NE;CE Mod<M>& OP*=(CO Mod<M>& n)NE;IN Mod<M>& OP/=(Mod<M> n);TE <TY INT> CE Mod<M>& OP<<=(INT n);TE <TY INT> CE Mod<M>& OP>>=(INT n);CE Mod<M>& OP++()NE;CE Mod<M> OP++(int)NE;CE Mod<M>& OP--()NE;CE Mod<M> OP--(int)NE;DC_OF_CM_FOR_MOD(==);DC_OF_CM_FOR_MOD(!=);DC_OF_CM_FOR_MOD(<);DC_OF_CM_FOR_MOD(<=);DC_OF_CM_FOR_MOD(>);DC_OF_CM_FOR_MOD(>=);DC_OF_AR_FOR_MOD(+,NE);DC_OF_AR_FOR_MOD(-,NE);DC_OF_AR_FOR_MOD(*,NE);DC_OF_AR_FOR_MOD(/,);TE <TY INT> CE Mod<M> OP^(INT EX)CO;TE <TY INT> CE Mod<M> OP<<(INT n)CO;TE <TY INT> CE Mod<M> OP>>(INT n)CO;CE Mod<M> OP-()CO NE;CE Mod<M>& SignInvert()NE;IN Mod<M>& Invert();TE <TY INT> CE Mod<M>& PW(INT EX);CE VO swap(Mod<M>& n)NE;CE CRUI RP()CO NE;ST CE Mod<M> DeRP(uint n)NE;ST IN CO Mod<M>& Inverse(CRUI n);ST IN CO Mod<M>& Factorial(CRUI n);ST IN CO Mod<M>& FactorialInverse(CRUI n);ST IN Mod<M> Combination(CRUI n,CRUI i);ST IN CO Mod<M>& zero()NE;ST IN CO Mod<M>& one()NE;ST IN CE uint GetModulo()NE;TE <TY INT> CE Mod<M>& PositivePW(INT EX)NE;TE <TY INT> CE Mod<M>& NonNegativePW(INT EX)NE;US COants = COantsForMod<M>;};
US MP = Mod<P>;
TE <uint M> CE Mod<M>::Mod()NE:m_n(){}TE <uint M> CE Mod<M>::Mod(CO Mod<M>& n)NE:m_n(n.m_n){}TE <uint M> CE Mod<M>::Mod(Mod<M>&& n)NE:m_n(MO(n.m_n)){}TE <uint M> TE <TY T,SFINAE_FOR_MOD> CE Mod<M>::Mod(T n)NE:m_n(Residue<M>(MO(n))){}TE <uint M> CE Mod<M>& Mod<M>::OP=(Mod<M> n)NE{m_n = MO(n.m_n);RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP+=(CO Mod<M>& n)NE{(m_n += n.m_n)< M?m_n:m_n -= M;RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP-=(CO Mod<M>& n)NE{m_n < n.m_n?(m_n += M)-= n.m_n:m_n -= n.m_n;RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP*=(CO Mod<M>& n)NE{m_n = MO(ull(m_n)* n.m_n)% M;RE *TH;}TE <> CE MP& MP::OP*=(CO MP& n)NE{ull m_n_copy = m_n;m_n = MO((m_n_copy *= n.m_n)< P?m_n_copy:ResidueP(m_n_copy));RE *TH;}TE <uint M> IN Mod<M>& Mod<M>::OP/=(Mod<M> n){RE OP*=(n.Invert());}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::OP<<=(INT n){AS(n >= 0);RE *TH *= Mod<M>(2).NonNegativePW(MO(n));}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::OP>>=(INT n){AS(n >=0);WH(n-- > 0){((m_n & 1)== 0?m_n:m_n += M)>>= 1;}RE *TH;}TE <uint M> CE Mod<M>& Mod<M>::OP++()NE{m_n < COants::g_M_minus?++m_n:m_n = 0;RE *TH;}TE <uint M> CE Mod<M> Mod<M>::OP++(int)NE{Mod<M> n{*TH};OP++();RE n;}TE <uint M> CE Mod<M>& Mod<M>::OP--()NE{m_n == 0?m_n = COants::g_M_minus:--m_n;RE *TH;}TE <uint M> CE Mod<M> Mod<M>::OP--(int)NE{Mod<M> n{*TH};OP--();RE n;}DF_OF_CM_FOR_MOD(==);DF_OF_CM_FOR_MOD(!=);DF_OF_CM_FOR_MOD(>);DF_OF_CM_FOR_MOD(>=);DF_OF_CM_FOR_MOD(<);DF_OF_CM_FOR_MOD(<=);DF_OF_AR_FOR_MOD(+,NE,n,+);DF_OF_AR_FOR_MOD(-,NE,n.SignInvert(),+);DF_OF_AR_FOR_MOD(*,NE,n,*);DF_OF_AR_FOR_MOD(/,,n.Invert(),*);TE <uint M> TE <TY INT> CE Mod<M> Mod<M>::OP^(INT EX)CO{RE MO(Mod<M>(*TH).PW(MO(EX)));}TE <uint M> TE <TY INT> CE Mod<M> Mod<M>::OP<<(INT n)CO{RE MO(Mod<M>(*TH)<<= MO(n));}TE <uint M> TE <TY INT> CE Mod<M> Mod<M>::OP>>(INT n)CO{RE MO(Mod<M>(*TH)>>= MO(n));}TE <uint M> CE Mod<M> Mod<M>::OP-()CO NE{RE MO(Mod<M>(*TH).SignInvert());}TE <uint M> CE Mod<M>& Mod<M>::SignInvert()NE{m_n > 0?m_n = M - m_n:m_n;RE *TH;}TE <uint M> IN Mod<M>& Mod<M>::Invert(){AS(m_n != 0);uint m_n_neg;RE m_n < COants::g_memory_LE?(m_n = Inverse(m_n).m_n,*TH):((m_n_neg = M - m_n)< COants::g_memory_LE)?(m_n = M - Inverse(m_n_neg).m_n,*TH):NonNegativePW(COants::g_order_minus_1);}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::PositivePW(INT EX)NE{Mod<M> PW{*TH};EX--;WH(EX != 0){(EX & 1)== 1?*TH *= PW:*TH;EX >>= 1;PW *= PW;}RE *TH;}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::NonNegativePW(INT EX)NE{RE EX == 0?(m_n = 1,*TH):PositivePW(MO(EX));}TE <uint M> TE <TY INT> CE Mod<M>& Mod<M>::PW(INT EX){bool neg = EX < 0;AS(!(neg && m_n == 0));RE neg?PositivePW(ll(MO(EX %= COants::g_M_minus))* COants::g_order_minus_1_neg %COants::g_M_minus):NonNegativePW(MO(EX));}TE <uint M> CE VO Mod<M>::swap(Mod<M>& n)NE{std::swap(m_n,n.m_n);}TE <uint M> IN CO Mod<M>& Mod<M>::Inverse(CRUI n){AS(n < M);ST VE<Mod<M>> memory ={zero(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory.push_back(DeRP(M - memory[M % LE_curr].m_n * ull(M / LE_curr)% M));LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::Factorial(CRUI n){if(M <= n){RE zero();}ST VE<Mod<M>> memory ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory.push_back(memory[LE_curr - 1]* LE_curr);LE_curr++;}RE memory[n];}TE <uint M> IN CO Mod<M>& Mod<M>::FactorialInverse(CRUI n){ST VE<Mod<M>> memory ={one(),one()};ST uint LE_curr = 2;WH(LE_curr <= n){memory.push_back(memory[LE_curr - 1]* Inverse(LE_curr));LE_curr++;}RE memory[n];}TE <uint M> IN Mod<M> Mod<M>::Combination(CRUI n,CRUI i){RE i <= n?Factorial(n)* FactorialInverse(i)* FactorialInverse(n - i):zero();}TE <uint M> CE CRUI Mod<M>::RP()CO NE{RE m_n;}TE <uint M> CE Mod<M> Mod<M>::DeRP(uint n)NE{Mod<M> n_copy{};n_copy.m_n = MO(n);RE n_copy;}TE <uint M> IN CO Mod<M>& Mod<M>::zero()NE{ST CE CO Mod<M> z{};RE z;}TE <uint M> IN CO Mod<M>& Mod<M>::one()NE{ST CE CO Mod<M> o{1};RE o;}TE <uint M> IN CE uint Mod<M>::GetModulo()NE{RE M;}TE <uint M> IN Mod<M> Inverse(CO Mod<M>& n){RE MO(Mod<M>(n).Invert());}TE <uint M,TY INT> CE Mod<M> PW(Mod<M> n,INT EX){RE MO(n.PW(MO(EX)));}TE <uint M> CE VO swap(Mod<M>& n0,Mod<M>& n1)NE{n0.swap(n1);}TE <uint M> IN string to_string(CO Mod<M>& n)NE{RE to_string(n.RP())+ " + " + to_string(M)+ "Z";}TE <uint M,CL Traits> IN IS& OP>>(IS& is,Mod<M>& n){ll m;is >> m;n = m;RE is;}TE <uint M,CL Traits> IN OS& OP<<(OS& os,CO Mod<M>& n){RE os << n.RP();}
#define DF_OF_HASH_FOR_MOD(MOD)IN size_t hash<MOD>::OP()(CO MOD& n)CO{ST CO hash<decldecay_t(n.RP())> h;RE h(n.RP());}
TE <uint M> DC_OF_HASH(Mod<M>); TE <uint M> DF_OF_HASH_FOR_MOD(Mod<M>);

/* Loop (1KB)*/
TE <TY INT> bool NextLoop(CRI SZ,CO VE<INT>& lower_bound,CO VE<INT>& upper_limit,VE<INT>& index){int depth = 0;WH(depth < SZ){if(++index[depth]< upper_limit[depth]){break;}index[depth]= lower_bound[depth];depth++;}RE depth < SZ;}TE <TY INT> bool NextLoop(CO VE<INT>& lower_bound,CO VE<INT>& upper_limit,VE<INT>& index){RE NextLoop(index.SZ(),lower_bound,upper_limit,index);}TE <TY INT> bool NextLoopEq(CRI SZ,CO VE<INT>& lower_bound,CO VE<INT>& upper_bound,VE<INT>& index){int depth = 0;WH(depth < SZ){if(++index[depth]<= upper_bound[depth]){break;}index[depth]= lower_bound[depth];depth++;}RE depth < SZ;}TE <TY INT> bool NextLoopEq(CO VE<INT>& lower_bound,CO VE<INT>& upper_bound,VE<INT>& index){RE NextLoopEq(index.SZ(),lower_bound,upper_bound,index);}

/* string (1KB)*/
TE <TY INT> IN char IntToChar(CO INT& i,CO char& c = 'a'){RE c + i;}TE <TY INT> IN INT CharToInt(CO char& i){RE i -(i < 'a'?'A':'a');}TE <TY INT>string ArrayToString(CO VE<INT>& A,CO char& c = 'a'){CO int N = A.SZ();string S(N,c);for(int i = 0;i < N;i++){S[i]= IntToChar<INT>(A[i],c);}RE S;}TE <TY INT>VE<INT> StringToArray(CO string& S){CO int N = S.SZ();VE<int> A(N);for(int i = 0;i < N;i++){A[i]= CharToInt<INT>(S[i]);}RE A;}
#endif
/* AAA 常設ライブラリは以上に挿入する。*/

#define INCLUDE_LIBRARY
#include __FILE__
#endif /* INCLUDE_LIBRARY */
#endif /* INCLUDE_SUB */
#endif /* INCLUDE_MAIN */
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