High School Programming League 2010/11

Given 8 integers: -1000 < x₁, y₁, x₂, y₂, x₃, y₃, x₄, y₄ < 1000.

Check what is the shape of the intersection of two axis-aligned rectangles: P1 = (x₁, y₁), (x₁, y₂), (x₂, y₂), (x₂, y₁) and P2 = (x₃, y₃), (x₃, y₄), (x₄, y₄), (x₄, y₃).

• If the rectangles do not intersect print nothing.
• If there is exactly one point in common print point.
• If the intersections of P1 and P2 is a line segment print line.
• If they have a rectangular area in common print rectangle.

Input data specification

The first line contains the number of test cases t (1<=t<1000). Each of the following t lines contains 8 integers: x₁, y₁, x₂, y₂, x₃, y₃, x₄, y₄.

The area of both rectangles is greater than 0.

Output data specification

For each test case print one word on a separate line: nothing, point, line or rectangle.

Example

Input:
5
1 1 2 2 2 2 3 3
10 1 1 10 12 9 10 12
2 3 10 10 1 4 0 0
1 20 20 1 2 10 10 2
10 20 20 10 20 30 25 1

Output:
point
line
nothing
rectangle
line

Scoring

By solving this problem you will score 10 points.

Bonus challenge

The registered contestant who solves the problem in the least number of bytes of source code will receive a small gift.