Description

A very important and complicated machine consists of n wheels, numbered l, 2, . . . , n. They

are actually cogwheels, but the cogs are so small that we can model them as circles on the plane.

Every wheel can spin around its center.

Two wheels cannot overlap (they do not have common interior points), but they can touch.

If two wheels touch each other and one of them rotates, the other one spins as well, as their

micro-cogs are locked together.

A force is put to wheel I (and to no other wheel), making it rotate at the rate of exactly

one turn per minute, clockwise. Compute the rates of other wheels7 movement. You mav assume

that the machine is not jammed (the movement is physically possible).

给出平面上的n个齿轮，忽略齿的大小。它们不能有交集，但可以相切。当用T=1的速度推动1号齿轮时（相切的转动，可以传动），求每个齿轮的转速。你可以假定机器不会卡死。

n<=1000

其余数字<=10000

Format

Input

The first line of input contains the number of test cases T. The descriptions of the test cases

follow:

Each test case consists of one line containing the number of wheels n (1《 n≤ 1000) . Each

of the following lines contain three integers x, y and r (-10 000 < x, y < 10 000; I≤ r≤ 10 000)

where (x, y) denote the Cartesian coordinates of the wheel's center and r is its radius.

Output

For each test case, output n lines, each describing the movement of one wheel, in the same

order as in the input. For every wheel, output either p/q clockwise or p/q counterclockwise,

where the irreducible fraction p/q is the number of wheel turns per minute. If q is l, output just

p as an integer. If a wheel is standing still, output not moving.

Samples

1
5
0 0 6
6 8 4
-9 0 3
6 16 4
0- 11 4

1 clockwise
3/2 counterclockwise
2 counterclockwise
3/2 clockwise
not moving