You are given 2 objects, and you're trying to figure out collisions!

You might be given 2 rectangles, and you want to know if the rectangles overlap or not.

You might also be given 2 circles, and you want to know if the circles overlap or not.

Constraints

~1 \leq r,l,w \leq 10^6~

~-10^6 \leq x,y,h,k \leq 10^6~

Input Specifications

The first line of input will be a string that is either circle or rectangle.

If the first line is circle, there will be 2 lines of input, with each line containing space-separated integers ~h,k,r~, a circle with center ~(h,k)~ and radius ~r~.

If the first line is rectangle, there will be 2 lines of input, with each line containing space-separated integers ~x,y,l,w~, a rectangle with bottome left corner ~(x,y)~, length (horizontally) ~l~ and width (vertically) ~w~.

Output Specifications

If the first line of input is circle, output overlapping if the circles overlap (including tangency!), or non-overlapping if the circles are not overlapping.

If the first line of input is rectangle, output overlapping if the rectangles overlap (including touching on the edges or corners!), or non-overlapping if the rectangles are not intersecting.

Sample Input 1

circle
0 0 5
6 8 5

Sample Output 1

overlapping

Explanation for Sample Output 1

It can be shown that the only point where these circles intersect is at ~(3,4)~. Thus, the two circles are intersecting.

Sample Input 2

rectangle
0 0 2 2
2 2 4 4

Sample Output 2

overlapping

Explanation for Sample Output 2

It can be shown that the only point where these rectangles intersect is at ~(2,2)~. Thus, the two rectangles are intersecting.