Given two integers ~a~ and ~b~ representing the linear equation ~y = ax + b~, determine the direction of the line (increasing, decreasing, or horizontal).

The graph displays three lines with different directions: ~y = -x + 1~ (blue line) is a decreasing line due to a negative slope; ~y = x + 1~ (green line) is an increasing line due to a positive slope; ~y = 1~ (red line) is a horizontal line since the slope is zero.

Input

• The first line contains only integer ~t~ (~1 \le t \le 10^6~) - the number of testcase.
• ~t~ lines next, each line contains two integers ~a~ and ~b~ (~-10^9 \le a, b \le 10^9~).

Output

• Each testcase, print direction of linear equation: increasing, decreasing or horizontal.

Samples

Sample Input 1

3
1 1
-1 4
0 3

Sample Output 1

increasing
decreasing
horizontal