#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ); signal( SIGABRT , &AlertAbort )
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
  #define CERR( MESSAGE ) cerr << MESSAGE << endl;
  #define COUT( ANSWER ) cout << ANSWER << endl
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " << ( MIN ) << ( ( MIN ) <= A ? "<=" : ">" ) << A << ( A <= ( MAX ) ? "<=" : ">" ) << ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
#define LIBRARY_SEARCH bool searched_library = false; LibrarySearch( searched_library ); if( searched_library ){ QUIT; };
  #define START_WATCH( PROCESS_NAME ) StartWatch( PROCESS_NAME )
  #define STOP_WATCH( HOW_MANY_TIMES ) StopWatch( HOW_MANY_TIMES )
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr )
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
  #define CERR( MESSAGE ) 
  #define COUT( ANSWER ) cout << ANSWER << "\n"
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define LIBRARY_SEARCH
  #define START_WATCH( PROCESS_NAME )
  #define STOP_WATCH( HOW_MANY_TIMES )
#endif
// #define RANDOM_TEST
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define TYPE_OF( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN( LL , A ) LL A; cin >> A
#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define GETLINE( A ) string A; getline( cin , A )
#define GETLINE_SEPARATE( A , SEPARATOR ) string A; getline( cin , A , SEPARATOR )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- )
#define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end()
#define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define QUIT return 0
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )

#ifdef DEBUG
  inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); }
  void StartWatch( const string& process_name = "nothing" );
  void StopWatch( const int& how_many_times = 1 );
#endif
#if defined( DEBUG ) && defined( RANDOM_TEST )
  inline CEXPR( int , bound_random_test_num , 1000 );
  #define START_MAIN FOR( random_test_num , 0 , bound_random_test_num ){ CERR( "(" << random_test_num << ")" );
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  #define SET_ASSERT( A , MIN , MAX ) CERR( #A << " = " << ( A = GetRand( MIN , MAX ) ) )
  #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ( ANSWER ) << " == " << guchoku ); continue; } else { CERR( ( ANSWER ) << " != " << guchoku ); QUIT; }
  #define FINISH_MAIN CERR( "" ); }
#else
  #define START_MAIN 
  #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX )
  #define RETURN( ANSWER ) COUT( ( ANSWER ) ); QUIT
  #define FINISH_MAIN 
#endif

template <typename T> inline T Absolute( const T& a ){ return a > 0 ? a : -a; }
template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT );	\
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;			\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;	\
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO )		\
  ll ANSWER{ 1 };							\
  {									\
    ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( MODULO ) + ( ( ARGUMENT ) % ( MODULO ) ) ) % ( MODULO ); \
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \
  static ll ANSWER[CONSTEXPR_LENGTH];					\
  static ll ANSWER_INV[CONSTEXPR_LENGTH];				\
  static ll INVERSE[CONSTEXPR_LENGTH];					\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_INDEX ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \
    }									\
    ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
    FOREQ( i , 2 , MAX_INDEX ){						\
      ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \
    }									\
  }									\

// 二分探索テンプレート
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  if( MINIMUM <= MAXIMUM ){						\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM;				\
    ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH;			\
    while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \
      CERR( "二分探索中： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "=" << VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){	\
	VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U;			\
      } else {								\
	VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L;			\
      }									\
      ANSWER = UPDATE_ANSWER;						\
    }									\
    CERR( "二分探索終了： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) << TARGET ); \
    CERR( ( EXPRESSION DESIRED_INEQUALITY TARGET ? "二分探索成功" : "二分探索失敗" ) ); \
    assert( EXPRESSION DESIRED_INEQUALITY TARGET );			\
  } else {								\
    CERR( "二分探索失敗： " << MINIMUM << ">" << MAXIMUM );		\
    assert( MINIMUM <= MAXIMUM );					\
  }									\

// 単調増加の時にEXPRESSION >= TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調増加の時にEXPRESSION <= TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION >= TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \
    
// 単調減少の時にEXPRESSION <= TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

template <typename T>
class CoordinateCompress
{

private:
  vector<T> m_a;
  map<T,int> m_enum;
  bool m_compressed;
  int m_size;

public:
  inline CoordinateCompress();
  template <typename U , int length_max> inline CoordinateCompress( const U ( &a )[length_max] , const int& length );
  template <typename U> inline CoordinateCompress( const vector<U>& a );

  inline void Insert( const T& t );
  template <typename U , int length_max> inline void Insert( const U ( &a )[length_max] , const int& length );
  template <typename U> inline void Insert( const vector<U>& a );

  inline const T& GetSmallest( const int& i = 0 );
  inline const T& GetLargest( const int& i = 0 );
  inline int GetOrder( const T& t );
  inline const int& size();

  inline typename map<T,int>::iterator begin();
  inline typename map<T,int>::iterator end();

private:
  inline void Compress();
  
};

template <typename T> inline CoordinateCompress<T>::CoordinateCompress() : m_a() , m_enum() , m_compressed() , m_size() {}
template <typename T> template <typename U , int length_max> inline CoordinateCompress<T>::CoordinateCompress( const U ( &a )[length_max] , const int& length ) : CoordinateCompress() { Insert( a , length ); }
template <typename T> template <typename U> inline CoordinateCompress<T>::CoordinateCompress( const vector<U>& a ) : CoordinateCompress() { Insert( a ); }

template <typename T> inline void CoordinateCompress<T>::Insert( const T& t ) { m_enum[t]; m_size = m_enum.size(); m_compressed = false; }
template <typename T> template <typename U , int length_max> inline void CoordinateCompress<T>::Insert( const U ( &a )[length_max] , const int& length ) { assert( length <= length_max ); if( length > 0 ){ for( int i = 0 ; i < length ; i++ ){ m_enum[ a[i] ]; } m_size = m_enum.size(); m_compressed = false; } }
template <typename T> template <typename U> inline void CoordinateCompress<T>::Insert( const vector<U>& a ) { const int length = a.size(); if( length > 0 ){ for( int i = 0 ; i < length ; i++ ){ m_enum[ a[i] ]; } m_size = m_enum.size(); m_compressed = false; } }

template <typename T> inline const T& CoordinateCompress<T>::GetSmallest( const int& i ) { if( ! m_compressed ){ Compress(); } assert( i < m_size ); return m_a[i]; }
template <typename T> inline const T& CoordinateCompress<T>::GetLargest( const int& i ) { if( ! m_compressed ){ Compress(); } assert( i < m_size ); return m_a[m_size - i - 1]; }
template <typename T> inline int CoordinateCompress<T>::GetOrder( const T& t ) { if( ! m_compressed ){ Compress(); } return m_enum.count( t ) == 1 ? m_enum[t] : -1; }
template <typename T> inline const int& CoordinateCompress<T>::size() { return m_size; }

template <typename T> inline typename map<T,int>::iterator CoordinateCompress<T>::begin() { return m_enum.begin(); }
template <typename T> inline typename map<T,int>::iterator CoordinateCompress<T>::end() { return m_enum.end(); }

template <typename T> inline void CoordinateCompress<T>::Compress() { m_a.resize( m_size ); m_size = 0; for( auto itr = m_enum.begin() , end = m_enum.end() ; itr != end ; itr++ ){ m_a[itr->second = m_size++] = itr->first; } m_compressed = true; }

class CoordinateStack
{

private:
  vector<int> m_length;
  int m_size;
  
public:
  inline CoordinateStack();
  inline CoordinateStack( const int& size );

  inline int& length( const int& n );
  inline const int& size() const noexcept;

  inline void push_back( const int& length );
  inline void pop_back();
  inline void resize( const int& size );

  inline int GetOrder( const int& n , const int& i ) const;
  inline pair<int,int> GetOrder( const int& n , const int& i , const int& j ) const;

};

inline CoordinateStack::CoordinateStack() : m_length( 1 ) , m_size() {}
inline CoordinateStack::CoordinateStack( const int& size ) : m_length( 1 + size ) , m_size( size ) {}

inline int& CoordinateStack::length( const int& n ) { assert( n < m_size ); return m_length[1 + n]; }
inline const int& CoordinateStack::size() const noexcept { return m_size; }

inline void CoordinateStack::push_back( const int& length ) { m_length.push_back( length ); m_size++; }
inline void CoordinateStack::pop_back() { assert( m_size > 0 ); m_length.pop_back(); m_size--; }
inline void CoordinateStack::resize( const int& size ) { m_length.resize( 1 + size ); m_size = size; }

inline int CoordinateStack::GetOrder( const int& n , const int& i ) const { return m_length[n] + i; }
inline pair<int,int> CoordinateStack::GetOrder( const int& n , const int& i , const int& j ) const { const int& length_n = m_length[n]; return { length_n + i , length_n + j }; }

// 配列の各要素がint型の範疇でも総和がそうでない場合はTをint型にすると正しく動作しないことに注意。
// InitialSegmentSumで負の入力を扱うためにuintではなくintをテンプレート引数にする。

// 使用演算：
// T& T::operator=( const T& )
// T& T::operator+=( const T& )
// T operator-( const T& , const T& )（ただしIntervalSumを用いない場合は不要）
// T operator<( const T& , const T& )（ただしBinarySearchを用いない場合は不要）
template <typename T , int N>
class BIT
{
private:
  T m_fenwick[N + 1];

public:
  inline BIT();
  BIT( const T ( & a )[N] );

  // const参照でないことに注意。
  inline T Get( const int& i ) const;
  inline void Set( const int& i , const T& n );
  inline void Set( const T ( & a )[N] );

  inline BIT<T,N>& operator+=( const T ( & a )[N] );
  void Add( const int& i , const T& n );

  T InitialSegmentSum( const int& i_final ) const;
  inline T IntervalSum( const int& i_start , const int& i_final ) const;
  
  // operator+=の単位元T()より小さくない要素のみを成分に持つ場合のみサポート。
  // InitialSegmentSum( i )がn以上となるiが存在する場合にその最小値を2進法で探索。
  int BinarySearch( const T& n ) const;
  // IntervalSum( i_start , i )がt以上となるi_start以上のiが存在する場合にその最小値を2進法で探索。
  inline int BinarySearch( const int& i_start , const T& n ) const;
  
};

template <typename T , int N> inline BIT<T,N>::BIT() : m_fenwick() {}
template <typename T , int N>
BIT<T,N>::BIT( const T ( & a )[N] ) : m_fenwick()
{

  for( int j = 1 ; j <= N ; j++ ){

    T& fenwick_j = m_fenwick[j];
    int i = j - 1;
    fenwick_j = a[i];
    int i_lim = j - ( j & -j );

    while( i != i_lim ){

      fenwick_j += m_fenwick[i];
      i -= ( i & -i );

    }

  }

}

template <typename T , int N> inline T BIT<T,N>::Get( const int& i ) const { return IntervalSum( i , i ); }
template <typename T , int N> inline void BIT<T,N>::Set( const int& i , const T& n ) { Add( i , n - IntervalSum( i , i ) ); }
template <typename T , int N> inline void BIT<T,N>::Set( const T ( & a )[N] ) { BIT<T,N> a_copy{ a }; swap( m_fenwick , a_copy.m_fenwick ); }

template <typename T , int N> inline BIT<T,N>& BIT<T,N>::operator+=( const T ( & a )[N] ) { for( int i = 0 ; i < N ; i++ ){ Add( i , a[i] ); } return *this; }

template <typename T , int N>
void BIT<T,N>::Add( const int& i , const T& n )
{
  
  int j = i + 1;

  while( j <= N ){

    m_fenwick[j] += n;
    j += ( j & -j );

  }

  return;
  
}

template <typename T , int N> 
T BIT<T,N>::InitialSegmentSum( const int& i_final ) const
{

  T sum = 0;
  int j = ( i_final < N ? i_final : N - 1 ) + 1;

  while( j > 0 ){

    sum += m_fenwick[j];
    j -= j & -j;
    
  }

  return sum;
  
}

template <typename T , int N> inline T BIT<T,N>::IntervalSum( const int& i_start , const int& i_final ) const { return InitialSegmentSum( i_final ) - InitialSegmentSum( i_start - 1 ); }

// 使用演算：
// T& T::operator=( const T& )（BITそのものに使用）
// T& T::operator+=( const T& )
// T& operator+( const T& , const T& )
// T operator-( const T& )
// T operator-( const T& , const T& )
template <typename T , int N>
class IntervalAddBIT
{
private:
  // 母関数の微分の負の階差数列（(i-1)a_{i-1} - ia_i）の管理
  BIT<T,N> m_bit_0;
  // 階差数列（a_i - a_{i-1}）の管理
  BIT<T,N> m_bit_1;

public:
  inline IntervalAddBIT();
  inline IntervalAddBIT( const T ( &a )[N] );

  // const参照でないことに注意。
  inline T Get( const int& i ) const;
  inline void Set( const int& i , const T& n );
  inline void Set( const T ( &a )[N] );

  inline IntervalAddBIT<T,N>& operator+=( const T ( & a )[N] );
  inline void Add( const int& i , const T& n );
  inline void IntervalAdd( const int& i_start , const int& i_final , const T& n );

  inline T InitialSegmentSum( const int& i_final ) const;
  inline T IntervalSum( const int& i_start , const int& i_final ) const;
  
};

template <typename T , int N> inline IntervalAddBIT<T,N>::IntervalAddBIT() : m_bit_0() , m_bit_1() {}
template <typename T , int N> inline IntervalAddBIT<T,N>::IntervalAddBIT( const T ( &a )[N] ) : m_bit_0() , m_bit_1() { operator+=( a ); }

template <typename T , int N> inline T IntervalAddBIT<T,N>::Get( const int& i ) const { return IntervalSum( i , i ); }
template <typename T , int N> inline void IntervalAddBIT<T,N>::Set( const int& i , const T& n ) { Add( i , n - IntervalSum( i , i ) ); }
template <typename T , int N> inline void IntervalAddBIT<T,N>::Set( const T ( &a )[N] ) { IntervalAddBIT<T,N> a_copy{ a }; swap( m_bit_0 , a_copy.m_bit_0 ); swap( m_bit_1 , a_copy.m_bit_1 ); }

template <typename T , int N> inline IntervalAddBIT<T,N>& IntervalAddBIT<T,N>::operator+=( const T ( & a )[N] ) { for( int i = 0 ; i < N ; i++ ){ Add( i , a[i] ); } return *this; }

template <typename T , int N> inline void IntervalAddBIT<T,N>::Add( const int& i , const T& n ) { IntervalAdd( i , i , n ); }

template <typename T , int N> inline void IntervalAddBIT<T,N>::IntervalAdd( const int& i_start , const int& i_final , const T& n ) { m_bit_0.Add( i_start , - ( i_start - 1 ) * n ); m_bit_0.Add( i_final + 1 , i_final * n ); m_bit_1.Add( i_start , n ); m_bit_1.Add( i_final + 1 , - n ); }


template <typename T , int N> inline T IntervalAddBIT<T,N>::InitialSegmentSum( const int& i_final ) const { return m_bit_0.InitialSegmentSum( i_final ) + i_final * m_bit_1.InitialSegmentSum( i_final ); }

template <typename T , int N> inline T IntervalAddBIT<T,N>::IntervalSum( const int& i_start , const int& i_final ) const { return InitialSegmentSum( i_final ) - InitialSegmentSum( i_start - 1 ); }

// inline CEXPR( int , bound_N , 10 );
inline DEXPR( int , bound_N , 100000 , 100 ); // 0が5個
// inline CEXPR( int , bound_N , 1000000000 ); // 0が9個
// inline CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個
TYPE_OF( bound_N ) N;

// // inline CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N );
// // inline CEXPR( int , bound_M , 10 );
// inline DEXPR( int , bound_M , 100000 , 100 ); // 0が5個
// // inline CEXPR( int , bound_M , 1000000000 ); // 0が9個
// // inline CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個
// TYPE_OF( bound_M ) M;

// inline DEXPR( int , bound_H , 1000 , 10 );
// // inline DEXPR( int , bound_H , 100000 , 10 ); // 0が5個
// // inline CEXPR( int , bound_H , 1000000000 ); // 0が9個
// inline CEXPR( int , bound_W , bound_H );
// #if bound_H < ( 1 << 16 )
//   inline CEXPR( int , bound_HW , bound_H * bound_W );
// #else
//   inline CEXPR( ll , bound_HW , ll( bound_H ) * bound_W );
// #endif
// // CEXPR( int , bound_HW , 100000 ); // 0が5個
// // CEXPR( int , bound_HW , 1000000000 ); // 0が5個
// int H , W;
// inline int EnumHW( const int& h , const int& w ) { return h * W + w; }
// inline pair<int,int> EnumHW_inv( const int& v ) { return { v / W , v % W }; }
// inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[bound_HW] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW(i,j);if(i>0){e[EnumHW(i-1,j)].push_back(v);}if(i+1<H){e[EnumHW(i+1,j)].push_back(v);}if(j>0){e[EnumHW(i,j-1)].push_back(v);}if(j+1<W){e[EnumHW(i,j+1)].push_back(v);}}}}
// const string direction[4] = {"U","R","D","L"};
// inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);}
// inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW_inv(v);auto [k,h]=EnumHW_inv(w);return DirectionNumberOnGrid(i,j,k,h);}
// inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;}

// list<int> e[bound_N];
// // list<int> e[bound_HW];
// list<int> E( const int& i )
// {
//   list<int> answer = e[i];
//   // 入力によらない処理
//   return answer;
// }

// template <typename T> inline T add( const T& t0 , const T& t1 ) { return t0 + t1; }
// template <typename T> inline const T& zero() { static const T z = 0; return z; }
// template <typename T> inline T multiply( const T& t0 , const T& t1 ) { return t0 * t1; }
// template <typename T> inline const T& one() { static const T o = 1; return o; }

// inline CEXPR( ll , P , 998244353 );
// inline CEXPR( ll , P , 1000000007 );

int main()
{
  UNTIE;
  LIBRARY_SEARCH;
  START_MAIN;

  // DEXPR( int , bound_T , 100000 , 100 );
  // CIN_ASSERT( T , 1 , bound_T );
  // REPEAT( T ){

  // }

  // CIN( int , N );
  // // CIN( ll , N );
  SET_ASSERT( N , 1 , bound_N );
  // // CIN( int , M );
  // // CIN( ll , M );
  // SET_ASSERT( M , 1 , bound_M );
  // // CIN( int , K );
  // // CIN( ll , K );
  tuple<string,int,int> info[bound_N];
  map<string,CoordinateCompress<int> > cc{};
  CoordinateCompress<int> all_cc{};
  FOR( i , 0 , N ){
    CIN( string , X );
    CIN( int , L );
    CIN( int , R );
    info[i] = { X , L , R };
    auto& cc_X = cc[X];
    cc_X.Insert( L );
    cc_X.Insert( R );
    all_cc.Insert( L );
    all_cc.Insert( R );
  }

  // CIN( string , S );
  // CIN( string , T );

  // SET_ASSERT( H , 1 , bound_H );
  // SET_ASSERT( W , 1 , bound_W );
  // TYPE_OF( bound_HW ) HW = TYPE_OF( bound_HW )( H ) * W;
  // assert( HW <= bound_HW );
  
  // // CEXPR( int , bound_Ai , 10 );
  // // CEXPR( int , bound_Ai , 100000 ); // 0が5個
  // CEXPR( int , bound_Ai , 1000000000 ); // 0が9個
  // // CEXPR( ll , bound_Ai , 1000000000000000000 ); // 0が18個
  // // CEXPR( int , bound_Bi , bound_Ai );
  // int A[N];
  // ll A[N];
  // // int A[bound_N];
  // // ll A[bound_N];
  // int B[N];
  // // ll B[N];
  // // int B[bound_N];
  // // ll B[bound_N];
  // FOR( i , 0 , N ){
  //   CIN( int , Ai );
  //   // CIN( ll , Ai );
  //   // CIN_ASSERT( Ai , 0 , bound_Ai );
  //   A[i] = Ai;
  //   CIN( int , Bi );
  //   // CIN( ll , Bi );
  //   // CIN_ASSERT( Bi , 0 , bound_Bi );
  //   B[i] = Bi;
  // }

  // FOR( i , 0 , M ){
  //   CIN_ASSERT( ui , 1 , N );
  //   CIN_ASSERT( vi , 1 , N );
  //   ui--;
  //   vi--;
  //   e[ui].push_back( vi );
  //   e[vi].push_back( ui );
  // }

  // CIN( int , Q );
  DEXPR( int , bound_Q , 100000 , 100 );
  CIN_ASSERT( Q , 1 , bound_Q );
  tuple<int,string,int,int> query[bound_Q];
  FOR( q , 0 , Q ){
    CIN( int , type );
    if( type == 1 ){
      CIN( string , x );
      CIN( int , t );
      cc[x].Insert( t );
      all_cc.Insert( t );
      query[q] = { type , x , t , 0 };
    } else if( type == 2 ){
      CIN( int , t );
      all_cc.Insert( t );
      query[q] = { type , "" , t , 0 };
    } else {
      CIN( string , x );
      CIN( int , l );
      CIN( int , r );
      auto& cc_x = cc[x];
      cc_x.Insert( l );
      cc_x.Insert( r );
      all_cc.Insert( l );
      all_cc.Insert( r );
      query[q] = { type , x , l , r };
    }
  }
  CoordinateStack cs{};
  map<string,int> name{};
  int length = 0;
  FOR_ITR( cc ){
    name[itr->first] = length++;
    cs.push_back( itr->second.size() );
  }
  IntervalAddBIT<int,(bound_N+bound_Q)*2> come{};
  IntervalAddBIT<int,(bound_N+bound_Q)*2> count{};
  FOR( i , 0 , N ){
    auto& [X,L,R] = info[i];
    auto& cc_X = cc[X];
    auto [l,r] = cs.GetOrder( name[X] , cc_X.GetOrder( L ) , cc_X.GetOrder( R ) );
    come.IntervalAdd( l , r , 1 );
    count.IntervalAdd( all_cc.GetOrder( L ) , all_cc.GetOrder( R ) , 1 );
  }
  FOR( q , 0 , Q ){
    auto& [type,x,l,r] = query[q];
    if( type == 1 ){
      l = cs.GetOrder( name[x] , cc[x].GetOrder( l ) );
      COUT( ( come.IntervalSum( l , l ) > 0 ? "Yes" : "No" ) );
    } else if( type == 2 ){
      l = all_cc.GetOrder( l );
      COUT( ( count.IntervalSum( l , l ) ) );
    } else {
      auto& cc_x = cc[x];
      auto [L,R] = cs.GetOrder( name[x] , cc_x.GetOrder( l ) , cc_x.GetOrder( r ) );
      come.IntervalAdd( L , R , 1 );
      count.IntervalAdd( all_cc.GetOrder( l ) , all_cc.GetOrder( r ) , 1 );
    }
  }
  
  // ll guchoku = Guchoku();
  // ll answer = 0;

  // if( answer == guchoku ){
  //   CERR( answer << " == " << guchoku );
  // } else {
  //   CERR( answer << " != " << guchoku );
  //   QUIT;
  // }

  // COUT( ( answer ) );

  FINISH_MAIN;
  QUIT;
}