Fibonacci hater's hymn#5873
Sign in

Fibonacci hater's hymn

2 seconds
256 megabytes
Easy

Mr. Hamster harbors a strong dislike for Fibonacci. He doesn't just dislike the mathematician, but everything associated with him—especially the Fibonacci numbers. As a reminder, Fibonacci numbers are defined by the following rules:

f_0 = a;\quad f_1 = b;\quad f_i = f_{i-1} + f_{i-2},\quad i \geq 2

Additionally, Mr. Hamster is a fan of playing Nim and even organizes Nim competitions in his barn. However, he is adamant that no one is allowed to make a move in his barn that involves taking a number of stones equal to any Fibonacci number, even if such a move would secure a win.

Today, you are competing against Mr. Hamster. There are heaps of stones on the table in a game of Nim. Can you secure a win?

Input

The first line contains three integers: , , and (1 \leq a, b \leq 20, 1 \leq N \leq 10^5).

The second line contains the sizes of the heaps b_i (1 \leq b_i \leq 10^6).

Output

If you can win, print I hate Fibonacci (without quotes). Otherwise, print I love Fibonacci (without quotes).

Examples

Example 1

Loading
Loading