#ifndef INCLUDE_MODE
#define INCLUDE_MODE
// #define REACTIVE
// #define USE_GETLINE
/* #define SUBMIT_ONLY */
#define DEBUG_OUTPUT
// #define SAMPLE_CHECK dummy
#endif
#ifdef INCLUDE_MAIN
VO Solve()
{
CEXPR( int , p , int(1e9)+7 );
CIN_AA( Mod , 0 , 2 , 0 , 2 , A );
CIN_AA( Mod
, 0 , 2 , 0 , 2 , B );
RETURN( TwoByTwoSimilar( A , B ) ? "Yes" : "No" );
}
REPEAT_MAIN(1);
#else /* INCLUDE_MAIN */
#ifdef INCLUDE_SUB
// /* COMPAREに使用。圧縮時は削除する。*/
// MP Naive( int N , int M , int K , const vector& A , const bool& debug_output = true )
// // MP Naive( ll N , ll M , ll K , const vector& A , const bool& debug_output = true )
// {
// MP answer{};
// return answer;
// }
// /* COMPAREに使用。圧縮時は削除する。*/
// MP Answer( int N , int M , int K , const vector& A , const bool& debug_output = true )
// // MP Answer( ll N , ll M , ll K , const vector& A , 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
CERR( "全ての出力が一致しました。" );
}
/* 圧縮時は中身だけ削除する。*/
IN VO RandomTest( const int& test_case_num )
{
// 数 ../Contest/Template/RandomTest/Number.txt
// 配列 ../Contest/Template/RandomTest/Array.txt
// 順列 ../Contest/Template/RandomTest/Permutation.txt
// 文字列 ../Contest/Template/RandomTest/String.txt
// グリッド ../Contest/Template/RandomTest/Grid.txt
// グラフ ../Contest/Template/RandomTest/Graph.txt
// 重み付きグラフ ../Contest/Template/RandomTest/WeightedGraph.txt
// 区間クエリ ../Contest/Template/RandomTest/IntervalQuery.txt
// 多種クエリ ../Contest/Template/RandomTest/MultiTypeQuery.txt
REPEAT( test_case_num ){
}
CERR( "全ての出力が一致しました。" );
}
#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。*/
template
pair,vector> TwoByTwoSimilarity( const vector>& A )
{
assert( A.size() == 2 && A[0].size() == 2 && A[1].size() == 2 );
const T& one = T::one();
if( A[0][1] != 0 || A[1][0] != 0 || A[0][0] != A[1][1] ){
return { { one } , { A[0][0] * A[1][1] - A[0][1] * A[1][0] , - ( A[0][0] + A[1][1] ) , one } };
}
return { { -A[0][0] , one } , { -A[1][1] , one } };
}
template inline bool TwoByTwoSimilar( const MAT& A , const MAT& B ) { return TwoByTwoSimilarity( A ) == TwoByTwoSimilarity( B ); }
/* 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 DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 )
#define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) )
#define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , test_case_num_bound , BOUND ); int test_case_num = 1; if CE( test_case_num_bound > 1 ){ FINISH_MAIN
#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__ )
#define FINISH_MAIN GETLINE( test_case_num_str ); test_case_num = stoi( test_case_num_str ); ASSERT( test_case_num , 1 , test_case_num_bound ); } REPEAT( test_case_num ){ Solve(); } }
#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 __VA_ARGS__; SET_A( I , N , __VA_ARGS__ )
#define CIN_AA( LL , I0 , N0 , I1 , N1 , VAR ) VE> VAR( N0 + I0 ); FOR( VARIABLE_FOR_CIN_AA , 0 , N0 ){ SET_A( I1 , N1 , VAR[VARIABLE_FOR_CIN_AA + I0] ); }
#define FINISH_MAIN SET_ASSERT( test_case_num , 1 , test_case_num_bound ); } REPEAT( test_case_num ){ Solve(); } }
#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 )
#define TLE( CONDITION ) if( !( CONDITION ) ){ ll TLE_VAR = 1; while( TLE_VAR != 0 ){ ( TLE_VAR += 2 ) %= int( 1e9 ); } cerr << TLE_VAR << endl; }
#define MLE( CONDITION ) if( !( CONDITION ) ){ vector> MLE_VAR{}; REPEAT( 1e6 ){ MLE_VAR.push_back( vector( 1e6 ) ); } cerr << MLE_VAR << endl; }
#define OLE( CONDITION ) if( !( CONDITION ) ){ REPEAT( 1e8 ){ cerr << "OLE\n"; } }
#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
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 = loop_average_time , current_time = loop_start_time; int loop_count = current_time; assert( loop_count == 0 )
#define CURRENT_TIME ( current_time = static_cast( chrono::duration_cast( 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 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( N1 + I1 ) ); SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX )
#define PR1( A1 , ... ) A1
#define PR2( A1 , A2 , ... ) A2
#define PR3( A1 , A2 , A3 , ... ) A3
#define FOR_( VAR , INITIAL , FINAL , UPPER , COMP , INCR ) for( decldecay_t( UPPER ) VAR = INITIAL ; VAR COMP FINAL ; VAR INCR )
#define FOR( VAR , INITIAL , ... ) FOR_( VAR , INITIAL , PR1( __VA_ARGS__ ) , PR1( __VA_ARGS__ ) , < , PR3( __VA_ARGS__ , += PR2( __VA_ARGS__ , ? ) , ++ ) )
#define FOREQ( VAR , INITIAL , ... ) FOR_( VAR , INITIAL , PR1( __VA_ARGS__ ) , PR1( __VA_ARGS__ ) , <= , PR3( __VA_ARGS__ , += PR2( __VA_ARGS__ , ? ) , ++ ) )
#define FOREQINV( VAR , INITIAL , ... ) FOR_( VAR , INITIAL , PR1( __VA_ARGS__ ) , INITIAL , + 1 > , PR3( __VA_ARGS__ , -= PR2( __VA_ARGS__ , ? ) , -- ) )
#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 ){ CERR( "出力の不一致が検出されました。" ); RE; }
#define CHECK( ... ) auto answer = Answer( __VA_ARGS__ , false ); CERR( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Answer == " , answer )
/* 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
#define OS basic_ostream
#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
TE US ret_t = decltype(declval()(declval()...));
TE 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;
/* 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::value && ! is_same::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 >= CO_TARGETの最小解を格納。
#define MIN_GEQ(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,>=,CO_TARGET,>=,AN,AN + 1,(AN ## _L + AN ## _R)>> 1)
// 単調増加の時にEXPRESSION <= CO_TARGETの最大解を格納。
#define MAX_LEQ(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,<=,CO_TARGET,>,AN - 1,AN,(AN ## _L + 1 + AN ## _R)>> 1)
// 単調減少の時にEXPRESSION >= CO_TARGETの最大解を格納。
#define MAX_GEQ(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,>=,CO_TARGET,<,AN - 1,AN,(AN ## _L + 1 + AN ## _R)>> 1)
// 単調減少の時にEXPRESSION <= CO_TARGETの最小解を格納。
#define MIN_LEQ(AN,MINIMUM,MAXIMUM,EXPRESSION,CO_TARGET)BS(AN,MINIMUM,MAXIMUM,EXPRESSION,<=,CO_TARGET,<=,AN,AN + 1,(AN ## _L + AN ## _R)>> 1)
/* 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> 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(CRL Rand_min,CRL Rand_max){AS(Rand_min <= Rand_max);ll AN = time(NULL);RE AN * rand()%(Rand_max + 1 - Rand_min)+ Rand_min;}
/* Set (2KB)*/
#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 ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE ST CE CO bool value = is_same_v< decltype(Check(declval())),true_type >;};
TE US Set = conditional_t>,unordered_set,conditional_t,set,VO>>;
#define DF_OF_POP_FOR_SET(SET)TE IN T pop_max(SET& S){AS(!S.empty());auto IT = --S.EN();T AN = *IT;S.erase(IT);RE AN;}TE IN T pop_min(SET& S){AS(!S.empty());auto IT = S.BE();T AN = *IT;S.erase(IT);RE AN;}TE IN SET& OP<<=(SET& S,T t){S.insert(MO(t));RE S;}TE IN SET& OP<<=(SET& S,U&& u){S.insert(T{forward(u)});RE S;}TE IN SET& OP>>=(SET& S,CO T& t){auto IT = S.lower_bound(t);AS(IT != S.EN()&& *IT == t);S.erase(IT);RE S;}TE IN SET& OP>>=(SET& S,CO U& u){RE S >>= T{u};}TE IN CO T& Get(CO SET& S,int i){auto BE = S.BE(),EN = S.EN();auto& IT = i < 0?(++i,--EN):BE;WH(i > 0 && IT != EN){--i;++IT;}WH(i < 0 && IT != BE){++i;--IT;}AS(i == 0);RE *IT;}
#define DF_OF_UNION_FOR_SET(SET)TE IN SET& OP|=(SET& S0,SET S1){S0.merge(MO(S1));RE S0;}TE IN SET OP|(SET S0,SET S1){RE MO(S0.SZ()< S1.SZ()?S1 |= MO(S0):S0 |= MO(S1));}
TE IN TY SET::const_iterator MaximumLeq(CO SET& S,CO T& t){auto IT = S.upper_bound(t);RE IT == S.BE()?S.EN():--IT;}TE IN TY SET::const_iterator MaximumLt(CO SET& S,CO T& t){auto IT = S.lower_bound(t);RE IT == S.BE()?S.EN():--IT;}TE IN TY SET::const_iterator MinimumGeq(CO SET& S,CO T& t){RE S.lower_bound(t);}TE IN TY SET::const_iterator MinimumGt(CO SET& S,CO T& t){RE S.upper_bound(t);}TE IN VO EraseBack(SET& S,ITERATOR& IT){IT = S.erase(IT);}TE IN VO EraseFront(SET& S,ITERATOR& IT){IT = S.erase(IT);IT == S.BE()?IT = S.EN():--IT;}TE TY SET,TY T,TY...Args> IN bool In(CO SET& S,CO T& t){RE S.count(t)== 1;}DF_OF_POP_FOR_SET(set);DF_OF_POP_FOR_SET(unordered_set);DF_OF_POP_FOR_SET(multiset);DF_OF_POP_FOR_SET(unordered_multiset);DF_OF_UNION_FOR_SET(set);DF_OF_UNION_FOR_SET(unordered_set);DF_OF_UNION_FOR_SET(multiset);DF_OF_UNION_FOR_SET(unordered_multiset);DF_OF_UNION_FOR_SET(VE);DF_OF_UNION_FOR_SET(LI);
/* Tuple (6KB)*/
#define DF_OF_AR_FOR_TUPLE(OPR)TE TY PAIR> IN auto OP OPR ## =(PAIR& t0,CO PAIR& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = get<0>(t1);get<1>(t0)OPR ## = get<1>(t1);RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO TUPLE& t1)-> decltype((get<0>(t0),t0))&{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 TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO TUPLE& t1)-> decltype((get<0>(t0),t0))&{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 PAIR> IN auto OP OPR ## =(PAIR& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;RE t0;}TE TY TUPLE> IN auto OP OPR ## =(TUPLE& t0,CO ARG& t1)-> decltype((get<0>(t0),t0))&{get<0>(t0)OPR ## = t1;get<1>(t0)OPR ## = t1;get<2>(t0)OPR ## = t1;get<3>(t0)OPR ## = t1;RE t0;}TE TY TUPLE,TY...ARGS,TY ARG> IN auto OP OPR(CO TUPLE& 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 PAIR> IN auto OP INCR(PAIR& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);RE t;}TE TY TUPLE> IN auto OP INCR(TUPLE& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);RE t;}TE TY TUPLE> IN auto OP INCR(TUPLE& t)-> decltype((get<0>(t),t))&{INCR get<0>(t);INCR get<1>(t);INCR get<2>(t);INCR get<3>(t);RE t;}
TE IN IS& OP>>(IS& is,tuple& arg){RE is >> get<0>(arg);}TE TY V> IN auto OP>>(IS& is,V& arg)-> decltype((get<0>(arg),is))&{RE is >> get<0>(arg)>> get<1>(arg);}TE IN IS& OP>>(IS& is,tuple& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg);}TE IN IS& OP>>(IS& is,tuple& arg){RE is >> get<0>(arg)>> get<1>(arg)>> get<2>(arg)>> get<3>(arg);}TE IN OS& OP<<(OS& os,CO tuple& arg){RE os << get<0>(arg);}TE TY V> IN auto OP<<(OS& os,CO V& arg)-> decltype((get<0>(arg),os))&{RE os << get<0>(arg)<< " " << get<1>(arg);}TE IN OS& OP<<(OS& os,CO tuple& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg);}TE IN OS& OP<<(OS& os,CO tuple& arg){RE os << get<0>(arg)<< " " << get<1>(arg)<< " " << get<2>(arg)<< " " << get<3>(arg);}DF_OF_AR_FOR_TUPLE(+);TE TY V> IN auto OP-(CO V& t)-> decldecay_t((get<0>(t),t)){RE{-get<0>(t),-get<1>(t)};}TE IN tuple OP-(CO tuple& t){RE{-get<0>(t),-get<1>(t),-get<2>(t)};}TE IN tuple OP-(CO tuple& 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(--);
TE CL TupleAccessIndex{};TE CL Tuple:PU tuple{PU:IN Tuple(Types&&... args);TE IN Tuple(Args&&... args);TE IN auto& OP[](CO TupleAccessIndex& i)NE;TE IN CO auto& OP[](CO TupleAccessIndex& i)CO NE;};TE CL tuple_size>:PU tuple_size>{};TE CL tuple_element>:PU tuple_element>{};
TE US Pair = Tuple;TE US T2 = Pair;TE US T3 = Tuple;TE US T4 = Tuple;
CE TupleAccessIndex<0> O{};CE TupleAccessIndex<1> I{};CE TupleAccessIndex<2> II{};CE TupleAccessIndex<3> III{};
TE IN Tuple::Tuple(Types&&... args):tuple(MO(args)...){}TE TE IN Tuple::Tuple(Args&&... args):tuple(forward(args)...){}TE TE IN auto& Tuple::OP[](CO TupleAccessIndex& i)NE{RE get(*TH);}TE TE IN CO auto& Tuple::OP[](CO TupleAccessIndex& i)CO NE{RE get(*TH);}
#define DF_OF_HASH_FOR_TUPLE(PAIR)TE IN size_t hash>::OP()(CO PAIR& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash h0;ST CO hash h1;RE(h0(get<0>(n))* seed)^ h1(get<1>(n));}
TE DC_OF_HASH(tuple);TE DC_OF_HASH(pair);TE DC_OF_HASH(tuple);TE DC_OF_HASH(tuple);TE DC_OF_HASH(tuple);
TE IN size_t hash>::OP()(CO tuple& n)CO{ST CO hash h;RE h(get<0>(n));}DF_OF_HASH_FOR_TUPLE(pair);DF_OF_HASH_FOR_TUPLE(tuple);TE IN size_t hash>::OP()(CO tuple& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash> h01;ST CO hash h2;RE(h01({get<0>(n),get<1>(n)})* seed)^ h2(get<2>(n));}TE IN size_t hash>::OP()(CO tuple& n)CO{ST CO size_t seed =(GetRand(1e3,1e8)<< 1)| 1;ST CO hash> h01;ST CO hash> h23;RE(h01({get<0>(n),get<1>(n)})* seed)^ h23({get<2>(n),get<3>(n)});}
/* Vector (3KB)*/
#define DF_OF_COUT_FOR_VE(V)TE IN OS& OP<<(OS& os,CO V& arg){auto BE = arg.BE(),EN = arg.EN();auto IT = BE;WH(IT != EN){(IT == BE?os:os << " ")<< *IT;IT++;}RE os;}
DF_OF_COUT_FOR_VE(VE);DF_OF_COUT_FOR_VE(LI);DF_OF_COUT_FOR_VE(set);DF_OF_COUT_FOR_VE(unordered_set);DF_OF_COUT_FOR_VE(multiset);IN VO VariadicResize(CRI SZ){}TE IN VO VariadicResize(CRI SZ,Arg& arg,ARGS&... args){arg.resize(SZ);VariadicResize(SZ,args...);}
#define DF_OF_AR_FOR_VE(V,OPR)TE IN V& OP OPR ## =(V& a0,CO V& 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 IN V& OP OPR ## =(V& a,CO T& t){for(auto& x:a){x OPR## = t;}RE a;}TE IN V OP OPR(V a,CO U& u){RE MO(a OPR ## = u);}
#define DF_OF_INCREMENT_FOR_VE(V,INCR)TE IN V& OP INCR(V& a){for(auto& i:a){INCR i;}RE a;}
#define DF_OF_SHIFT_FOR_VE(V)TE IN V& OP<<=(V& a,T t){a.push_back(MO(t));RE a;}TE IN V& OP<<=(V& a,U&& u){RE a <<= T{forward(u)};}TE IN T pop(V& a){AS(!a.empty());T AN = MO(a.back());a.pop_back();RE AN;}
#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 IN V OP-(V a){RE MO(a *= T(-1));}TE IN V OP*(CO T& t,V v){RE MO(v *= t);}DF_OF_SHIFT_FOR_VE(V);
DF_OF_ARS_FOR_VE(VE);DF_OF_ARS_FOR_VE(LI);DF_OF_SHIFT_FOR_VE(basic_string);
TE IN auto Get(V& a){RE[&](CRI i = 0)-> CO decldecay_t(a[0])&{RE a[i];};}TE IN VE id(CRI SZ){VE AN(SZ);for(int i = 0;i < SZ;i++){AN[i]= i;}RE AN;}TE IN VO Sort(V& a,CO bool& reversed = false){US T = decltype(a[0]);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 IN VO Sort(V0& a,V1& b,CO bool& reversed = false){CO int SZ = a.SZ();AS(SZ == int(b.SZ()));VE> v(SZ);for(int i = 0;i < SZ;i++){v[i]={MO(a[i]),MO(b[i])};}Sort(v,reversed);for(int i = 0;i < SZ;i++){a[i]= MO(v[i].first);b[i]= MO(v[i].second);}}TE IN VE IndexSort(CO V& a,CO bool& reversed = false){auto index = id(a.SZ());sort(index.BE(),index.EN(),[&](CRI i,CRI j){RE reversed?a[j]< a[i]:a[i]< a[j];});RE index;}TE IN int len(CO V& a){RE a.SZ();}TE IN VO Reverse(V& a){CO int SZ = len(a),half = SZ / 2;for(int i = 0;i < half;i++){swap(a[i],a[SZ-1-i]);}};TE IN V Reversed(V a){Reverse(a);RE MO(a);}
/* Map (1KB)*/
#define DF_OF_AR_FOR_MAP(MAP,OPR)TE IN MAP& OP OPR ## =(MAP& a,CO pair& v){a[v.first]OPR ## = v.second;RE a;}TE IN MAP& OP OPR ## =(MAP& a0,CO MAP& a1){for(auto&[t,u]:a1){a0[t]OPR ## = u;}RE a0;}TE IN MAP OP OPR(MAP 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 US Map = conditional_t>,unordered_map,conditional_t,map,VO>>;
DF_OF_ARS_FOR_MAP(map);DF_OF_ARS_FOR_MAP(unordered_map);
/* StdStream (2KB)*/
TE IN IS& VariadicCin(IS& is){RE is;}TE IN IS& VariadicCin(IS& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);}TE IN IS& VariadicSet(IS& is,CRI i){RE is;}TE IN IS& VariadicSet(IS& is,CRI i,Arg& arg,ARGS&... args){RE VariadicSet(is >> arg[i],i,args...);}TE IN IS& VariadicGetline(IS& is,CO char& separator){RE is;}TE IN IS& VariadicGetline(IS& is,CO char& separator,Arg& arg,ARGS&... args){RE VariadicGetline(getline(is,arg,separator),separator,args...);}TE IN OS& VariadicCout(OS& os,Arg&& arg){RE os << forward(arg);}TE IN OS& VariadicCout(OS& os,Arg1&& arg1,Arg2&& arg2,ARGS&&... args){RE VariadicCout(os << forward(arg1)<< " ",forward