Having surveyed his worktable once again, Petya suddenly understood the cause of all his recent failures: of course, the talisman! His usual talisman, the pink pig, apparently couldn't help him in the contest. Petya pondered over this problem and came out with a set of conditions for a new talisman:

1. The talisman must be a structure consisting of identical balls with a radius of 1 mm in 3-dimensional space; some of the balls must be connected by 8 mm long rods.
2. If two balls are connected by a chain of rods, then the minimal number of rods in a chain connecting these balls must be equal to the distance in centimeters between the centers of the balls.

Petya has developed a scheme describing the number of balls in his future talisman and the pairs of balls that must be connected by rods. Now he wants to write a program that will find if it is possible to construct a talisman according to this scheme. However, as Petya still doesn't have a proper talisman, he can't produce a working program. That is why Petya asks for your help.

The first line contains the number of balls N and the number of rods M in Petya's scheme (1 ≤ N ≤ 100; 0 ≤ M ≤ 10000). In the following M lines, pairs of balls connected by rods are given. The balls are numbered from 1 to N. For any two balls in the scheme, there is at most one rod connecting them; no ball is connected by a rod with itself.

If it is possible to construct a talisman by Petya's scheme, output “Luck is possible”; otherwise, output “Unlucky Petr”.