Rectangles (1) P56635

In a popular manager of windows, the following definition is used to mantain the information of the visible windows in the screen of the computer:

    struct Rectangle {
        int x_left, x_right, y_down, y_up;
    };

Here, the rectangles have the parallel sides in the axes @x@ and @y@, and @x_left@, @x_right@, @y_down@ and @y_up@ are respectively the minimal horitzontal coordenate, the maxmal horitzontal coordenate, the minimal vertical coordenate, and the maximal vertical coordenate of each rectangle.

Write a procedure that reads a rectangle:

    void read(Rectangle& r);

which is given in the input with the four integer numbers @x_left@, @x_right@, @y_down@ and @y_up@ in this order.

Write also a function that indicates the relationship that have two given rectangles @r1@ and @r2@:

    int relationship(const Rectangle& r1, const Rectangle& r2);

that must return 1 if @r@ is inside @r2@, 2 if @r2@ is inside @r1@, 3 if none is inside the other one but the rectangles intersect, 4 if the rectangles are identical, and 0 otherwise (if the rectangles do not have ay point in common).

Suppose that two rectangles intersect even if they coincide only in a segment or a point. Moreover, suppose that all the rectangles are correctly formed, that is, that @x_left@ is strictly smaller than @x_right@, and that @y_down@ is srictly smaller than @y_up@.

Use these definitions and procedures to write a program that reads a series of pairs of rectangles, and for each one prints which relationship have.

Input

Input consists of a natural $n$, followed by $n$ lines, each one with two rectangles (eight integer numbers).

Output

For each pair of rectangles, print their relationship as it is shown in the examples.