#include <iostream>
#include <set>
#include <map>
#include <limits>
#include <vector>

#include <iomanip>               // for std::setw
#include <ios>                   // for std::noskipws, streamsize
#include <istream>               // for std::istream
#include <ostream>               // for std::ostream
#include <sstream>               // for std::ostringstream
#include <cstddef>               // for NULL
#include <stdexcept>             // for std::domain_error
#include <string>                // for std::string implicit constructor
#include <cstdlib>               // for std::abs
#include <limits>                // for std::numeric_limits

#include<type_traits>

using namespace std;

# define throw(x) throw(x)
namespace boost {
    template<bool B, class T = void>
    struct enable_if_c {
        typedef T type;
    };

    template<class T>
    struct enable_if_c<false, T> {
    };

    template<bool B, class T = void>
    struct disable_if_c {
        typedef T type;
    };

    template<class T>
    struct disable_if_c<true, T> {
    };
};


#include <cassert>
#include <climits>
#include <iterator>
#include <algorithm>
#include <limits>
#include <type_traits>


namespace boost {

   template <class I>
   class rational;

   namespace integer {

      namespace gcd_detail{

         template <class T>
         inline constexpr T constexpr_min(T const& a, T const& b) noexcept
         {
            return a < b ? a : b;
         }
         template <class T>
         inline constexpr auto constexpr_swap(T&a, T& b) noexcept -> decltype(a.swap(b))
         {
            return a.swap(b);
         }
         template <class T, class U>
         inline constexpr void constexpr_swap(T&a, U& b...) noexcept
         {
            T t(static_cast<T&&>(a));
            a = static_cast<T&&>(b);
            b = static_cast<T&&>(t);
         }

      template <class T, bool a =
         std::is_unsigned<T>::value ||
         (std::numeric_limits<T>::is_specialized && !std::numeric_limits<T>::is_signed)>
      struct gcd_traits_abs_defaults
      {
         inline static constexpr const T& abs(const T& val) noexcept { return val; }
      };
      template <class T>
      struct gcd_traits_abs_defaults<T, false>
      {
         inline static T constexpr abs(const T& val) noexcept
         {
            // This sucks, but std::abs is not constexpr :(
            return val < T(0) ? -val : val;
         }
      };

      enum method_type
      {
         method_euclid = 0,
         method_binary = 1,
         method_mixed = 2
      };

      struct any_convert
      {
         template <class T>
         any_convert(const T&);
      };

      struct unlikely_size
      {
         char buf[9973];
      };

      unlikely_size operator <<= (any_convert, any_convert);
      unlikely_size operator >>= (any_convert, any_convert);

      template <class T>
      struct gcd_traits_defaults : public gcd_traits_abs_defaults<T>
      {
         inline static constexpr unsigned make_odd(T& val) noexcept
         {
            unsigned r = 0;
            while(0 == (val & 1u))
            {
               val >>= 1;
               ++r;
            }
            return r;
         }
         inline static constexpr bool less(const T& a, const T& b) noexcept
         {
            return a < b;
         }

         static T& get_value();

         static const bool has_operator_left_shift_equal = sizeof(get_value() <<= 2) != sizeof(unlikely_size);
         static const bool has_operator_right_shift_equal = sizeof(get_value() >>= 2) != sizeof(unlikely_size);
         static const method_type method = std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer && has_operator_left_shift_equal && has_operator_right_shift_equal ? method_mixed : method_euclid;
      };
      //
      // Default gcd_traits just inherits from defaults:
      //
      template <class T>
      struct gcd_traits : public gcd_traits_defaults<T> {};

   //
   // The Mixed Binary Euclid Algorithm
   // Sidi Mohamed Sedjelmaci
   // Electronic Notes in Discrete Mathematics 35 (2009) 169-176
   //
   template <class T>
   constexpr T mixed_binary_gcd(T u, T v) noexcept
   {
      if(gcd_traits<T>::less(u, v))
         constexpr_swap(u, v);

      unsigned shifts = 0;

      if(u == T(0))
         return v;
      if(v == T(0))
         return u;

      shifts = constexpr_min(gcd_traits<T>::make_odd(u), gcd_traits<T>::make_odd(v));

      while(gcd_traits<T>::less(1, v))
      {
         u %= v;
         v -= u;
         if(u == T(0))
            return v << shifts;
         if(v == T(0))
            return u << shifts;
         gcd_traits<T>::make_odd(u);
         gcd_traits<T>::make_odd(v);
         if(gcd_traits<T>::less(u, v))
            constexpr_swap(u, v);
      }
      return (v == 1 ? v : u) << shifts;
   }

    /** Stein gcd (aka 'binary gcd')
     *
     * From Mathematics to Generic Programming, Alexander Stepanov, Daniel Rose
     */
    template <typename SteinDomain>
    constexpr SteinDomain Stein_gcd(SteinDomain m, SteinDomain n) noexcept
    {
        assert(m >= 0);
        assert(n >= 0);
        if (m == SteinDomain(0))
            return n;
        if (n == SteinDomain(0))
            return m;
        // m > 0 && n > 0
        unsigned d_m = gcd_traits<SteinDomain>::make_odd(m);
        unsigned d_n = gcd_traits<SteinDomain>::make_odd(n);
        // odd(m) && odd(n)
        while (m != n)
        {
            if (n > m)
               constexpr_swap(n, m);
            m -= n;
            gcd_traits<SteinDomain>::make_odd(m);
        }
        // m == n
        m <<= constexpr_min(d_m, d_n);
        return m;
    }


    /** Euclidean algorithm
     *
     * From Mathematics to Generic Programming, Alexander Stepanov, Daniel Rose
     *
     */
    template <typename EuclideanDomain>
    inline constexpr EuclideanDomain Euclid_gcd(EuclideanDomain a, EuclideanDomain b) noexcept
    {
        while (b != EuclideanDomain(0))
        {
            a %= b;
            constexpr_swap(a, b);
        }
        return a;
    }


    template <typename T>
    inline constexpr typename enable_if_c<gcd_traits<T>::method == method_mixed, T>::type
       optimal_gcd_select(T const &a, T const &b) noexcept
    {
       return gcd_detail::mixed_binary_gcd(a, b);
    }

    template <typename T>
    inline constexpr typename enable_if_c<gcd_traits<T>::method == method_binary, T>::type
       optimal_gcd_select(T const &a, T const &b) noexcept
    {
       return gcd_detail::Stein_gcd(a, b);
    }

    template <typename T>
    inline constexpr typename enable_if_c<gcd_traits<T>::method == method_euclid, T>::type
       optimal_gcd_select(T const &a, T const &b) noexcept
    {
       return gcd_detail::Euclid_gcd(a, b);
    }

    template <class T>
    inline constexpr T lcm_imp(const T& a, const T& b) noexcept
    {
       T temp = boost::integer::gcd_detail::optimal_gcd_select(a, b);
       return (temp != T(0)) ? T(a / temp * b) : T(0);
    }

} // namespace detail


template <typename Integer>
inline constexpr Integer gcd(Integer const &a, Integer const &b) noexcept
{
    if(a == (std::numeric_limits<Integer>::min)())
       return a == static_cast<Integer>(0) ? gcd_detail::gcd_traits<Integer>::abs(b) : boost::integer::gcd(static_cast<Integer>(a % b), b);
    else if (b == (std::numeric_limits<Integer>::min)())
       return b == static_cast<Integer>(0) ? gcd_detail::gcd_traits<Integer>::abs(a) : boost::integer::gcd(a, static_cast<Integer>(b % a));
    return gcd_detail::optimal_gcd_select(static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(a)), static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(b)));
}

template <typename Integer>
inline constexpr Integer lcm(Integer const &a, Integer const &b) noexcept
{
   return gcd_detail::lcm_imp(static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(a)), static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(b)));
}

}  // namespace integer
}  // namespace boost


namespace boost {
namespace rational_detail{

   template <class FromInt, class ToInt>
   struct is_compatible_integer
   {
       static const bool value = ((std::numeric_limits<FromInt>::is_specialized && std::numeric_limits<FromInt>::is_integer
         && (std::numeric_limits<FromInt>::digits <= std::numeric_limits<ToInt>::digits)
         && (std::numeric_limits<FromInt>::radix == std::numeric_limits<ToInt>::radix)
         && ((std::numeric_limits<FromInt>::is_signed == false) || (std::numeric_limits<ToInt>::is_signed == true))
         && is_convertible<FromInt, ToInt>::value)
         || is_same<FromInt, ToInt>::value)
         || (is_class<ToInt>::value && is_class<FromInt>::value && is_convertible<FromInt, ToInt>::value);
   };

}

class bad_rational : public std::domain_error
{
public:
    explicit bad_rational() : std::domain_error("bad rational: zero denominator") {}
    explicit bad_rational( char const *what ) : std::domain_error( what ) {}
};

template <typename IntType>
class rational
{
    // Class-wide pre-conditions
    static_assert( ::std::numeric_limits<IntType>::is_specialized );

    // Helper types
    using param_type = IntType;

    struct helper { IntType parts[2]; };
    typedef IntType (helper::* bool_type)[2];

public:
    // Component type
    typedef IntType int_type;

    constexpr
    rational() : num(0), den(1) {}
    template <class T>
    constexpr rational(const T& n) : num(n), den(1) {}
    template <class T, class U>

    constexpr rational(const T& n, const U& d) : num(n), den(d) {
       normalize();
    }

    template < typename NewType >
    constexpr explicit
       rational(rational<NewType> const &r, typename enable_if_c<rational_detail::is_compatible_integer<NewType, IntType>::value>::type const* = 0)
       : num(r.numerator()), den(is_normalized(int_type(r.numerator()),
       int_type(r.denominator())) ? r.denominator() :
       (throw(bad_rational("bad rational: denormalized conversion")), 0)){}

    template < typename NewType >
    constexpr explicit
       rational(rational<NewType> const &r, typename disable_if_c<rational_detail::is_compatible_integer<NewType, IntType>::value>::type const* = 0)
       : num(r.numerator()), den(is_normalized(int_type(r.numerator()),
       int_type(r.denominator())) && is_safe_narrowing_conversion(r.denominator()) && is_safe_narrowing_conversion(r.numerator()) ? r.denominator() :
       (throw(bad_rational("bad rational: denormalized conversion")), 0)){}
    // Default copy constructor and assignment are fine

    // Add assignment from IntType
    template <class T>
    constexpr typename enable_if_c<
       rational_detail::is_compatible_integer<T, IntType>::value, rational &
    >::type operator=(const T& n) { return assign(static_cast<IntType>(n), static_cast<IntType>(1)); }

    // Assign in place
    template <class T, class U>
    constexpr typename enable_if_c<
       rational_detail::is_compatible_integer<T, IntType>::value && rational_detail::is_compatible_integer<U, IntType>::value, rational &
    >::type assign(const T& n, const U& d)
    {
       return *this = rational<IntType>(static_cast<IntType>(n), static_cast<IntType>(d));
    }
    //
    // The following overloads should probably *not* be provided -
    // but are provided for backwards compatibity reasons only.
    // These allow for construction/assignment from types that
    // are wider than IntType only if there is an implicit
    // conversion from T to IntType, they will throw a bad_rational
    // if the conversion results in loss of precision or undefined behaviour.
    //
    template <class T>
    constexpr rational(const T& n, typename enable_if_c<
       std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer
       && !rational_detail::is_compatible_integer<T, IntType>::value
       && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix)
       && is_convertible<T, IntType>::value
    >::type const* = 0)
    {
       assign(n, static_cast<T>(1));
    }
    template <class T, class U>
    constexpr rational(const T& n, const U& d, typename enable_if_c<
       (!rational_detail::is_compatible_integer<T, IntType>::value
       || !rational_detail::is_compatible_integer<U, IntType>::value)
       && std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer
       && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix)
       && is_convertible<T, IntType>::value &&
       std::numeric_limits<U>::is_specialized && std::numeric_limits<U>::is_integer
       && (std::numeric_limits<U>::radix == std::numeric_limits<IntType>::radix)
       && is_convertible<U, IntType>::value
    >::type const* = 0)
    {
       assign(n, d);
    }
    template <class T>
    constexpr typename enable_if_c<
       std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer
       && !rational_detail::is_compatible_integer<T, IntType>::value
       && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix)
       && is_convertible<T, IntType>::value,
       rational &
    >::type operator=(const T& n) { return assign(n, static_cast<T>(1)); }

    template <class T, class U>
    constexpr typename enable_if_c<
       (!rational_detail::is_compatible_integer<T, IntType>::value
          || !rational_detail::is_compatible_integer<U, IntType>::value)
       && std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer
       && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix)
       && is_convertible<T, IntType>::value &&
       std::numeric_limits<U>::is_specialized && std::numeric_limits<U>::is_integer
       && (std::numeric_limits<U>::radix == std::numeric_limits<IntType>::radix)
       && is_convertible<U, IntType>::value,
       rational &
    >::type assign(const T& n, const U& d)
    {
       if(!is_safe_narrowing_conversion(n) || !is_safe_narrowing_conversion(d))
          throw(bad_rational());
       return *this = rational<IntType>(static_cast<IntType>(n), static_cast<IntType>(d));
    }

    // Access to representation
    constexpr
    const IntType& numerator() const { return num; }
    constexpr
    const IntType& denominator() const { return den; }

    // Arithmetic assignment operators
    constexpr rational& operator+= (const rational& r);
    constexpr rational& operator-= (const rational& r);
    constexpr rational& operator*= (const rational& r);
    constexpr rational& operator/= (const rational& r);

    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator+= (const T& i)
    {
       num += i * den;
       return *this;
    }
    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator-= (const T& i)
    {
       num -= i * den;
       return *this;
    }
    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator*= (const T& i)
    {
       // Avoid overflow and preserve normalization
       IntType gcd = integer::gcd(static_cast<IntType>(i), den);
       num *= i / gcd;
       den /= gcd;
       return *this;
    }
    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator/= (const T& i)
    {
       // Avoid repeated construction
       IntType const zero(0);

       if(i == zero) throw(bad_rational());
       if(num == zero) return *this;

       // Avoid overflow and preserve normalization
       IntType const gcd = integer::gcd(num, static_cast<IntType>(i));
       num /= gcd;
       den *= i / gcd;

       if(den < zero) {
          num = -num;
          den = -den;
       }

       return *this;
    }

    // Increment and decrement
    constexpr const rational& operator++() { num += den; return *this; }
    constexpr const rational& operator--() { num -= den; return *this; }

    constexpr rational operator++(int)
    {
       rational t(*this);
       ++(*this);
       return t;
    }
    constexpr rational operator--(int)
    {
       rational t(*this);
       --(*this);
       return t;
    }

    // Operator not
    constexpr
    bool operator!() const { return !num; }

    // Boolean conversion

    constexpr
    operator bool_type() const { return operator !() ? 0 : &helper::parts; }


    // Comparison operators
    constexpr bool operator< (const rational& r) const;
    constexpr bool operator> (const rational& r) const { return r < *this; }
    constexpr
    bool operator== (const rational& r) const;

    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, bool>::type operator< (const T& i) const
    {
       // Avoid repeated construction
       int_type const  zero(0);

       // Break value into mixed-fraction form, w/ always-nonnegative remainder
       assert(this->den > zero);
       int_type  q = this->num / this->den, r = this->num % this->den;
       while(r < zero)  { r += this->den; --q; }

       // Compare with just the quotient, since the remainder always bumps the
       // value up.  [Since q = floor(n/d), and if n/d < i then q < i, if n/d == i
       // then q == i, if n/d == i + r/d then q == i, and if n/d >= i + 1 then
       // q >= i + 1 > i; therefore n/d < i iff q < i.]
       return q < i;
    }
    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, bool>::type operator>(const T& i) const
    {
       return operator==(i) ? false : !operator<(i);
    }
    template <class T>
    constexpr typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, bool>::type operator== (const T& i) const
    {
       return ((den == IntType(1)) && (num == i));
    }

private:
    // Implementation - numerator and denominator (normalized).
    // Other possibilities - separate whole-part, or sign, fields?
    IntType num;
    IntType den;

    // Helper functions
    static constexpr
    int_type inner_gcd( param_type a, param_type b, int_type const &zero =
     int_type(0) )
    { return b == zero ? a : inner_gcd(b, a % b, zero); }

    static constexpr
    int_type inner_abs( param_type x, int_type const &zero = int_type(0) )
    { return x < zero ? -x : +x; }

    // Representation note: Fractions are kept in normalized form at all
    // times. normalized form is defined as gcd(num,den) == 1 and den > 0.
    // In particular, note that the implementation of abs() below relies
    // on den always being positive.
    constexpr bool test_invariant() const;
    constexpr void normalize();

    static constexpr
    bool is_normalized( param_type n, param_type d, int_type const &zero =
     int_type(0), int_type const &one = int_type(1) )
    {
        return d > zero && ( n != zero || d == one ) && inner_abs( inner_gcd(n,
         d, zero), zero ) == one;
    }
    //
    // Conversion checks:
    //
    // (1) From an unsigned type with more digits than IntType:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits > std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T& val)
    {
       return val < (T(1) << std::numeric_limits<IntType>::digits);
    }
    //
    // (2) From a signed type with more digits than IntType, and IntType also signed:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits > std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == true), bool>::type is_safe_narrowing_conversion(const T& val)
    {
       // Note that this check assumes IntType has a 2's complement representation,
       // we don't want to try to convert a std::numeric_limits<IntType>::min() to
       // a T because that conversion may not be allowed (this happens when IntType
       // is from Boost.Multiprecision).
       return (val < (T(1) << std::numeric_limits<IntType>::digits)) && (val >= -(T(1) << std::numeric_limits<IntType>::digits));
    }
    //
    // (3) From a signed type with more digits than IntType, and IntType unsigned:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits > std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T& val)
    {
       return (val < (T(1) << std::numeric_limits<IntType>::digits)) && (val >= 0);
    }
    //
    // (4) From a signed type with fewer digits than IntType, and IntType unsigned:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T& val)
    {
       return val >= 0;
    }
    //
    // (5) From an unsigned type with fewer digits than IntType, and IntType signed:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == false) && (std::numeric_limits<IntType>::is_signed == true), bool>::type is_safe_narrowing_conversion(const T&)
    {
       return true;
    }
    //
    // (6) From an unsigned type with fewer digits than IntType, and IntType unsigned:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == false) && (std::numeric_limits<IntType>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T&)
    {
       return true;
    }
    //
    // (7) From an signed type with fewer digits than IntType, and IntType signed:
    //
    template <class T>
    constexpr static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == true), bool>::type is_safe_narrowing_conversion(const T&)
    {
       return true;
    }
};

// Unary plus and minus
template <typename IntType>
constexpr
inline rational<IntType> operator+ (const rational<IntType>& r)
{
    return r;
}

template <typename IntType>
constexpr
inline rational<IntType> operator- (const rational<IntType>& r)
{
    return rational<IntType>(static_cast<IntType>(-r.numerator()), r.denominator());
}

// Arithmetic assignment operators
template <typename IntType>
constexpr rational<IntType>& rational<IntType>::operator+= (const rational<IntType>& r)
{
    // This calculation avoids overflow, and minimises the number of expensive
    // calculations. Thanks to Nickolay Mladenov for this algorithm.
    //
    // Proof:
    // We have to compute a/b + c/d, where gcd(a,b)=1 and gcd(b,c)=1.
    // Let g = gcd(b,d), and b = b1*g, d=d1*g. Then gcd(b1,d1)=1
    //
    // The result is (a*d1 + c*b1) / (b1*d1*g).
    // Now we have to normalize this ratio.
    // Let's assume h | gcd((a*d1 + c*b1), (b1*d1*g)), and h > 1
    // If h | b1 then gcd(h,d1)=1 and hence h|(a*d1+c*b1) => h|a.
    // But since gcd(a,b1)=1 we have h=1.
    // Similarly h|d1 leads to h=1.
    // So we have that h | gcd((a*d1 + c*b1) , (b1*d1*g)) => h|g
    // Finally we have gcd((a*d1 + c*b1), (b1*d1*g)) = gcd((a*d1 + c*b1), g)
    // Which proves that instead of normalizing the result, it is better to
    // divide num and den by gcd((a*d1 + c*b1), g)

    // Protect against self-modification
    IntType r_num = r.num;
    IntType r_den = r.den;

    IntType g = integer::gcd(den, r_den);
    den /= g;  // = b1 from the calculations above
    num = num * (r_den / g) + r_num * den;
    g = integer::gcd(num, g);
    num /= g;
    den *= r_den/g;

    return *this;
}

template <typename IntType>
constexpr rational<IntType>& rational<IntType>::operator-= (const rational<IntType>& r)
{
    // Protect against self-modification
    IntType r_num = r.num;
    IntType r_den = r.den;

    // This calculation avoids overflow, and minimises the number of expensive
    // calculations. It corresponds exactly to the += case above
    IntType g = integer::gcd(den, r_den);
    den /= g;
    num = num * (r_den / g) - r_num * den;
    g = integer::gcd(num, g);
    num /= g;
    den *= r_den/g;

    return *this;
}

template <typename IntType>
constexpr rational<IntType>& rational<IntType>::operator*= (const rational<IntType>& r)
{
    // Protect against self-modification
    IntType r_num = r.num;
    IntType r_den = r.den;

    // Avoid overflow and preserve normalization
    IntType gcd1 = integer::gcd(num, r_den);
    IntType gcd2 = integer::gcd(r_num, den);
    num = (num/gcd1) * (r_num/gcd2);
    den = (den/gcd2) * (r_den/gcd1);
    return *this;
}

template <typename IntType>
constexpr rational<IntType>& rational<IntType>::operator/= (const rational<IntType>& r)
{
    // Protect against self-modification
    IntType r_num = r.num;
    IntType r_den = r.den;

    // Avoid repeated construction
    IntType zero(0);

    // Trap division by zero
    if (r_num == zero)
        throw(bad_rational());
    if (num == zero)
        return *this;

    // Avoid overflow and preserve normalization
    IntType gcd1 = integer::gcd(num, r_num);
    IntType gcd2 = integer::gcd(r_den, den);
    num = (num/gcd1) * (r_den/gcd2);
    den = (den/gcd2) * (r_num/gcd1);

    if (den < zero) {
        num = -num;
        den = -den;
    }
    return *this;
}


//
// Non-member operators: previously these were provided by Boost.Operator, but these had a number of
// drawbacks, most notably, that in order to allow inter-operability with IntType code such as this:
//
// rational<int> r(3);
// assert(r == 3.5); // compiles and passes!!
//
// Happens to be allowed as well :-(
//
// There are three possible cases for each operator:
// 1) rational op rational.
// 2) rational op integer
// 3) integer op rational
// Cases (1) and (2) are folded into the one function.
//
template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type
   operator + (const rational<IntType>& a, const Arg& b)
{
      rational<IntType> t(a);
      return t += b;
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type
   operator + (const Arg& b, const rational<IntType>& a)
{
      rational<IntType> t(a);
      return t += b;
}

template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type
   operator - (const rational<IntType>& a, const Arg& b)
{
      rational<IntType> t(a);
      return t -= b;
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type
   operator - (const Arg& b, const rational<IntType>& a)
{
      rational<IntType> t(a);
      return -(t -= b);
}

template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type
   operator * (const rational<IntType>& a, const Arg& b)
{
      rational<IntType> t(a);
      return t *= b;
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type
   operator * (const Arg& b, const rational<IntType>& a)
{
      rational<IntType> t(a);
      return t *= b;
}

template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type
   operator / (const rational<IntType>& a, const Arg& b)
{
      rational<IntType> t(a);
      return t /= b;
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type
   operator / (const Arg& b, const rational<IntType>& a)
{
      rational<IntType> t(b);
      return t /= a;
}

template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, bool>::type
   operator <= (const rational<IntType>& a, const Arg& b)
{
      return !(a > b);
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type
   operator <= (const Arg& b, const rational<IntType>& a)
{
      return a >= b;
}

template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, bool>::type
   operator >= (const rational<IntType>& a, const Arg& b)
{
      return !(a < b);
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type
   operator >= (const Arg& b, const rational<IntType>& a)
{
      return a <= b;
}

template <class IntType, class Arg>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, bool>::type
   operator != (const rational<IntType>& a, const Arg& b)
{
      return !(a == b);
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type
   operator != (const Arg& b, const rational<IntType>& a)
{
      return !(b == a);
}

template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type
   operator < (const Arg& b, const rational<IntType>& a)
{
      return a > b;
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type
   operator > (const Arg& b, const rational<IntType>& a)
{
      return a < b;
}
template <class Arg, class IntType>
constexpr
inline typename boost::enable_if_c <
   rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type
   operator == (const Arg& b, const rational<IntType>& a)
{
      return a == b;
}

// Comparison operators
template <typename IntType>
constexpr
bool rational<IntType>::operator< (const rational<IntType>& r) const
{
    // Avoid repeated construction
    int_type const  zero( 0 );

    // This should really be a class-wide invariant.  The reason for these
    // checks is that for 2's complement systems, INT_MIN has no corresponding
    // positive, so negating it during normalization keeps it INT_MIN, which
    // is bad for later calculations that assume a positive denominator.
    assert( this->den > zero );
    assert( r.den > zero );

    // Determine relative order by expanding each value to its simple continued
    // fraction representation using the Euclidian GCD algorithm.
    struct { int_type  n, d, q, r; }
     ts = { this->num, this->den, static_cast<int_type>(this->num / this->den),
     static_cast<int_type>(this->num % this->den) },
     rs = { r.num, r.den, static_cast<int_type>(r.num / r.den),
     static_cast<int_type>(r.num % r.den) };
    unsigned  reverse = 0u;

    // Normalize negative moduli by repeatedly adding the (positive) denominator
    // and decrementing the quotient.  Later cycles should have all positive
    // values, so this only has to be done for the first cycle.  (The rules of
    // C++ require a nonnegative quotient & remainder for a nonnegative dividend
    // & positive divisor.)
    while ( ts.r < zero )  { ts.r += ts.d; --ts.q; }
    while ( rs.r < zero )  { rs.r += rs.d; --rs.q; }

    // Loop through and compare each variable's continued-fraction components
    for ( ;; )
    {
        // The quotients of the current cycle are the continued-fraction
        // components.  Comparing two c.f. is comparing their sequences,
        // stopping at the first difference.
        if ( ts.q != rs.q )
        {
            // Since reciprocation changes the relative order of two variables,
            // and c.f. use reciprocals, the less/greater-than test reverses
            // after each index.  (Start w/ non-reversed @ whole-number place.)
            return reverse ? ts.q > rs.q : ts.q < rs.q;
        }

        // Prepare the next cycle
        reverse ^= 1u;

        if ( (ts.r == zero) || (rs.r == zero) )
        {
            // At least one variable's c.f. expansion has ended
            break;
        }

        ts.n = ts.d;         ts.d = ts.r;
        ts.q = ts.n / ts.d;  ts.r = ts.n % ts.d;
        rs.n = rs.d;         rs.d = rs.r;
        rs.q = rs.n / rs.d;  rs.r = rs.n % rs.d;
    }

    // Compare infinity-valued components for otherwise equal sequences
    if ( ts.r == rs.r )
    {
        // Both remainders are zero, so the next (and subsequent) c.f.
        // components for both sequences are infinity.  Therefore, the sequences
        // and their corresponding values are equal.
        return false;
    }
    else
    {
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4800)
#endif
        // Exactly one of the remainders is zero, so all following c.f.
        // components of that variable are infinity, while the other variable
        // has a finite next c.f. component.  So that other variable has the
        // lesser value (modulo the reversal flag!).
        return ( ts.r != zero ) != static_cast<bool>( reverse );
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
    }
}

template <typename IntType>
constexpr
inline bool rational<IntType>::operator== (const rational<IntType>& r) const
{
    return ((num == r.num) && (den == r.den));
}

// Invariant check
template <typename IntType>
constexpr
inline bool rational<IntType>::test_invariant() const
{
    return ( this->den > int_type(0) ) && ( integer::gcd(this->num, this->den) ==
     int_type(1) );
}

// Normalisation
template <typename IntType>
constexpr void rational<IntType>::normalize()
{
    // Avoid repeated construction
    IntType zero(0);

    if (den == zero)
       throw(bad_rational());

    // Handle the case of zero separately, to avoid division by zero
    if (num == zero) {
        den = IntType(1);
        return;
    }

    IntType g = integer::gcd(num, den);

    num /= g;
    den /= g;

    if (den < -(std::numeric_limits<IntType>::max)()) {
        throw(bad_rational("bad rational: non-zero singular denominator"));
    }

    // Ensure that the denominator is positive
    if (den < zero) {
        num = -num;
        den = -den;
    }

    assert( this->test_invariant() );
}

#ifndef BOOST_NO_IOSTREAM
namespace detail {

    // A utility class to reset the format flags for an istream at end
    // of scope, even in case of exceptions
    struct resetter {
        resetter(std::istream& is) : is_(is), f_(is.flags()) {}
        ~resetter() { is_.flags(f_); }
        std::istream& is_;
        std::istream::fmtflags f_;      // old GNU c++ lib has no ios_base
    };

}

// Input and output
template <typename IntType>
std::istream& operator>> (std::istream& is, rational<IntType>& r)
{
    using std::ios;

    IntType n = IntType(0), d = IntType(1);
    char c = 0;
    detail::resetter sentry(is);

    if ( is >> n )
    {
        if ( is.get(c) )
        {
            if ( c == '/' )
            {
                if ( is >> std::noskipws >> d )
                    try {
                        r.assign( n, d );
                    } catch ( bad_rational & ) {        // normalization fail
                        try { is.setstate(ios::failbit); }
                        catch ( ... ) {}  // don't throw ios_base::failure...
                        if ( is.exceptions() & ios::failbit )
                            throw;   // ...but the original exception instead
                        // ELSE: suppress the exception, use just error flags
                    }
            }
            else
                is.setstate( ios::failbit );
        }
    }

    return is;
}

// Add manipulators for output format?
template <typename IntType>
std::ostream& operator<< (std::ostream& os, const rational<IntType>& r)
{
    // The slash directly precedes the denominator, which has no prefixes.
    std::ostringstream  ss;

    ss.copyfmt( os );
    ss.tie( NULL );
    ss.exceptions( std::ios::goodbit );
    ss.width( 0 );
    ss << std::noshowpos << std::noshowbase << '/' << r.denominator();

    // The numerator holds the showpos, internal, and showbase flags.
    std::string const   tail = ss.str();
    std::streamsize const  w =
        os.width() - static_cast<std::streamsize>( tail.size() );

    ss.clear();
    ss.str( "" );
    ss.flags( os.flags() );
    ss << std::setw( w < 0 || (os.flags() & std::ios::adjustfield) !=
                     std::ios::internal ? 0 : w ) << r.numerator();
    return os << ss.str() + tail;
}
#endif  // BOOST_NO_IOSTREAM

// Type conversion
template <typename T, typename IntType>
constexpr
inline T rational_cast(const rational<IntType>& src)
{
    return static_cast<T>(src.numerator())/static_cast<T>(src.denominator());
}

// Do not use any abs() defined on IntType - it isn't worth it, given the
// difficulties involved (Koenig lookup required, there may not *be* an abs()
// defined, etc etc).
template <typename IntType>
constexpr
inline rational<IntType> abs(const rational<IntType>& r)
{
    return r.numerator() >= IntType(0)? r: -r;
}

} // namespace boost

using rational = boost::rational<unsigned long long>;

struct Teacup {
    unsigned long long temperature;
    rational volume;

    Teacup(int temperature, rational volume) : temperature(temperature), volume(volume) {}

    bool operator==(const Teacup& second) const noexcept {
        return this->temperature == second.temperature;
    }

    bool operator<(const Teacup& second) const noexcept {
        return this->temperature < second.temperature;
    }
};

ostream& operator<<(ostream& os, const Teacup& teacup)
{
    os << "(t: " << teacup.temperature << ", v: " << teacup.volume << ")";
    return os;
}

//ostream& operator<<(ostream& os, const pair<int,int>& teacup)
//{
//    os << "(t: " << teacup.first << ", v: " << teacup.second << ")";
//    return os;
//}

ostream& operator<<(ostream& os, const pair<rational, rational>& teacup)
{
    os << "(t: " << teacup.first << ", v: " << teacup.second << ")";
    return os;
}

//#define DEBUG

#ifdef DEBUG
#define dbg cerr
#else
#define dbg 0 && cerr
#endif


template<typename T>
void clear_with_zeros(T& mapa) {
    std::vector<rational> keys_to_remove;

    for(const auto& [key, value]: mapa) {
        if (value == 0ull) {
            keys_to_remove.push_back(key);
        }
    }

    for (const auto& key: keys_to_remove) {
        mapa.erase(key);
    }
}

bool solve() {
    int n;
    cin >> n;

    map<rational, rational> all_start, all_end;

    for (int i = 0; i < n; ++i) {
        int l, start, end;
        cin >> l >> start >> end;

        if (all_start.count(1ull * start) == 0) {
            all_start[1ull * start] = 0;
        }

        if (all_end.count(1ull* end) == 0) {
            all_end[1ull* end] = 0;
        }

        all_start[1ull* start] += 1ull* l;
        all_end[1ull* end] += 1ull* l;
    }

#ifdef DEBUG
    dbg << "Start: ";
    for(const auto& x: all_start) {
        dbg << x << " ";
    }
    dbg << endl << endl << "End: ";
    for(const auto& x: all_end) {
        dbg << x << " ";
    }
    dbg << endl << endl;
#endif

    // satisfy correct cups
    for(auto& [temp, volume]: all_end) {
        if (all_start.count(temp) > 0) {
            auto min = std::min(volume, all_start[temp]);

            volume -= min;
            all_start[temp] -= min;
        }
    }

    // clear with zero value
    clear_with_zeros(all_start);
    clear_with_zeros(all_end);

#ifdef DEBUG
    dbg << "\nStart: ";
    for(const auto& x: all_start) {
        dbg << x << " ";
    }
    dbg << endl << endl << "End: ";
    for(const auto& x: all_end) {
        dbg << x << " ";
    }
    dbg << endl << endl;
#endif

    if (all_start.size() == 0) {
        if (all_end.size() == 0) {
            return true;
        }
        return false;
    }
    if (all_end.size() == 0) {
        return false;
    }

    if (all_start.begin()->first > all_end.begin()->first) {
        return false;
    }
    if (all_start.rbegin()->first < all_end.rbegin()->first) {
        return false;
    }

    {
        rational power_total_start, power_total_end;
        for (const auto&[temp, volume]: all_start) {
            power_total_start += temp * volume;
        }
        for (const auto&[temp, volume]: all_end) {
            power_total_end += temp * volume;
        }

        if (power_total_start != power_total_end) {
            return false;
        }
    }


    while (all_end.size() > 1 && all_start.size() > 1) {
        dbg << endl;

        auto now = all_end.begin();
#ifdef DEBUG
        dbg << "Trying now " << *now << endl;
        dbg << "Using: ";
        for(const auto x: all_start) {
            dbg << x << " ";
        }
        dbg << endl;
#endif


        auto s1 = all_start.begin(), s2 = s1;
        s2++;

#define TEMP(x) (x->first)
#define VOL(x) (x->second)


        if (TEMP(now) < TEMP(s1)) {
            return false;
        }


        if (TEMP(now) > TEMP(s2)) {
            // merge s1 and s2

            auto vol = VOL(s1) + VOL(s2);
            auto temp = (TEMP(s1) * VOL(s1) + TEMP(s2) * VOL(s2)) / vol;

            all_start[temp] = vol;

            dbg << "Merge " << *s1 << " and " << *s2 << " into " << temp << ", " << vol << endl;

            all_start.erase(s1);
            all_start.erase(s2);

            continue;
        }

        // here, TEMP(s1) < TEMP(now) < TEMP(s2)
        // calculate how much to take from s1 and s2

        auto Ax1 = VOL(now) * (TEMP(s2) - TEMP(now)) / (TEMP(s2) - TEMP(s1));
        auto Ax2 = VOL(now) * (TEMP(now) - TEMP(s1)) / (TEMP(s2) - TEMP(s1));

        dbg << "Best to take " << Ax1 << " from first, and " << Ax2 << " from second" << endl;

        auto A1 = Ax1;
        auto A2 = Ax2;

        if (Ax1 > VOL(s1)) {
            A1 = VOL(s1);
            A2 = Ax2 * VOL(s1) / Ax1;
        }

        Ax1 = A1;
        Ax2 = A2;

        if (Ax2 > VOL(s2)) {
            A1 = Ax1 * VOL(s2) / Ax2;
            A2 = VOL(s2);
        }

        assert(Ax1 <= VOL(s1));

        dbg << "After reduction: " << A1 << ", " << A2 << endl;

        VOL(s1) -= A1;
        VOL(s2) -= A2;
        VOL(now) -= (A1 + A2);

        if (VOL(s1) == 0ull) {
            dbg << "dropping first!" << endl;
            all_start.erase(s1);
        }

        if (VOL(s2) == 0ull) {
            dbg << "dropping second!" << endl;
            all_start.erase(s2);
        }

        if (VOL(now) == 0ull) {
            dbg << "dropping requirement!" << endl;
            all_end.erase(now);
        }
    }

#ifdef DEBUG
    dbg << "\nAt the end:\n";

    dbg << "Start: ";
    for(const auto& x: all_start) {
        dbg << x << " ";
    }
    dbg << endl << endl << "End: ";
    for(const auto& x: all_end) {
        dbg << x << " ";
    }
    dbg << endl << endl;
#endif

    rational power_total_start, power_total_end;
    rational volume_total_start, volume_total_end;
    for(const auto& [temp, volume]: all_start) {
        power_total_start += temp*volume;
        volume_total_start += volume;
    }
    for(const auto& [temp, volume]: all_end) {
        power_total_end += temp*volume;
        volume_total_end += volume;
    }

    if (power_total_start == power_total_end && volume_total_start == volume_total_end) {
        return true;
    } else {
        return false;
    }
}

int main() {
//    std::ios_base::sync_with_stdio(false);
//    std::cin.tie(nullptr);

    int Z;
    cin >> Z;
    while(Z--) {
        if (solve()) {
            cout << "TAK\n";
        } else {
            cout << "NIE\n";
        }
    }
}