# Rectangles (1) P56635

Statement html

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:

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.

Public test cases
• Input

```6
2 3 4 6       0 5 2 8
0 10 0 10     9 10 0 1
0 2 0 2       1 3 1 3
-1 1 -2 2     -1 1 -2 2
0 1 0 2       5 7 4 7
0 2 0 2       2 4 2 4
```

Output

```the first rectangle is inside the second one
the second rectangle is inside the first one
rectangles intersect
rectangles are identical
rectangles do not intersect
rectangles intersect
```
• Information
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