Practice Mathematics and Geometry with the exercise "Die Handedness"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

According to Wikipedia (https://en.wikipedia.org/wiki/Dice):

"Opposite sides of a modern die traditionally add up to seven, requiring the 1, 2, and 3 faces to share a vertex. The faces of a die may be placed clockwise or counterclockwise about this vertex. If the 1, 2, and 3 faces run counterclockwise, the die is called "right-handed". If those faces run clockwise, the die is called "left-handed"."

You are given a die. You need to decide if it is right-handed or left-handed. If opposite sides don't add up to 7, we will say that the die is degenerate.

Input

The die is given as a 3-line string such as


 1
2354
 6

where the first and third lines have a whitespace in front. The arrangement contains all the numbers 1-6 exactly once.

Output

In a 1-line answer you need to output one of right-handed, left-handed and degenerate.

Constraints

Example

Input

 1
2354
 6

Output

right-handed

Solve it

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