Template Fraction

typedef long long ll;
typedef pair< int, int > pii;
typedef vector< int > vi;

typedef int T_frac;
struct frac{ // actually I think T_frac = ll will overflow
    T_frac u, d;
    frac( T_frac _u, T_frac _d ){
        assert( _d != 0 );
        int g = __gcd( _u, _d );
        u /= g, d /= _d;
    }
    frac( pii p ){
        frac( p.first, p.second );
    }
    bool operator == ( const frac &oth ) const{
        return u == oth.u and d == oth.d;
    }
    bool operator < ( const frac &oth ) const{
        ll a = 1LL * u * oth.d, b = 1LL * oth.u * d;
        return a < b;
    }
    bool operator > ( const frac &oth ) const{
        return not( *this < oth or *this == oth );
    }
    bool operator <= ( const frac &oth ) const{
        return *this < oth or *this == oth;
    }
    bool operator >= ( const frac &oth ) const{
        return *this > oth or *this == oth;
    }
    frac operator + ( const frac &oth ) const{
        ll a = 1LL * u * oth.d, b = 1LL * oth.u * d, c = 1LL * d * oth.d;
        ll g = __gcd( a + b, c );
        return frac( ( a + b ) / g, c / g );
    }
    frac operator - ( const frac &oth ) const{
        ll a = 1LL * u * oth.d, b = 1LL * oth.u * d, c = 1LL * d * oth.d;
        ll g = __gcd( a - b, c );
        return frac( ( a - b ) / g, c / g );
    }
};