#include doesn't work under Cygwin

#include <Python.h> doesn't work under Cygwin

Tried compiling the example from the beginning of this Python documentation article with gcc in Cygwin. My code:
#include <Python.h>

static PyObject *
spam_system(PyObject *self, PyObject *args)
{
    const char *command;
    int sts;

    if (!PyArg_ParseTuple(args, "s", &command))
        return NULL;
    sts = system(command);
    return PyLong_FromLong(sts);
}
However, when trying to compile, gcc gives me the following error:
In file included from /usr/include/Python.h:77:0,
                 from test.c:1:
/usr/include/longobject.h:77:26: error: expected '=', ',', ';', 'asm' or '__attr
ibute__' before 'PyLong_AsLongLong'
/usr/include/longobject.h:78:35: error: expected '=', ',', ';', 'asm' or '__attr
ibute__' before 'PyLong_AsUnsignedLongLong'
/usr/include/longobject.h:79:35: error: expected '=', ',', ';', 'asm' or '__attr
ibute__' before 'PyLong_AsUnsignedLongLongMask'
/usr/include/longobject.h:80:26: error: expected '=', ',', ';', 'asm' or '__attr
ibute__' before 'PyLong_AsLongLongAndOverflow'
Any ideas?
Update:
Apparently this is caused by PY_LONG_LONG expanding to __int64, which is not defined unless I include windows.h before Python.h. However, I don't see why that should be necessary, and it violates the following rule from the linked article: "Since Python may define some pre-processor definitions which affect the standard headers on some systems, you must include Python.h before any standard headers are included."
Is there any way to avoid having to include windows.h?