bool get( int n, unsigned char *r, int ix )
{
    return ( r[ ix / 8 ] >> ( ix % 8 ) ) & 0x01;
}

void set( int n, unsigned char *r, int ix )
{
    r[ ix / 8 ] |= 0x01 << ( ix % 8 );
}

int index( int n, int i, int j )
{
    return n * i + j;
}

bool add_transitivity( int n, unsigned char *r )
{
    bool changed = false;

    for ( int i = 0; i < n; ++ i )
    {
        for ( int j = 0; j < n; ++ j )
        {
            if ( !get( n, r, index( n, i, j ) ) )
                continue;

            for ( int k = 0; k < n; ++ k )
            {
                if ( !get( n, r, index( n, i, k ) ) &&
                        get( n, r, index( n, j, k ) ) )
                {
                    changed = true;
                    set( n, r, index( n, i, k ) );
                }
            }
        }
    }

    return changed;
}

void make_transitive( int n, unsigned char *r )
{
    while ( add_transitivity( n, r ) )
        ;
}