Fibonacci hater's hymn

"Hatred – disfigures the faces of the young, Hatred – bursts from its banks, Hatred – thirsts and wants to drink The black blood of enemies!" V.S. Vysotsky

Mr. Hamster has a strong dislike for Fibonacci. It's not just the mathematician he detests, but everything related to him, especially Fibonacci numbers. To remind you, Fibonacci numbers are defined by the following rule:

[ f_0 = a;  f_1 = b;  f_i = f_i-1 + f_i-2,  i $\ge$ 2 ]

Additionally, Mr. Hamster is a fan of playing Nim and even organizes Nim competitions in his barn. He is adamant that no one should make a move in his barn that involves taking a number of stones equal to any Fibonacci number, even if it means winning the game.

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

Input

The first line contains 3 integers: a, b, and N (1 ≤ a, b ≤ 20, 1 ≤ N ≤ 10^5).

The second line lists the sizes of the heaps b_i (1 ≤ b_i ≤ 10^6).

Output

If you can win, print "I hate Fibonacci" without quotes. If not, print "I love Fibonacci", also without quotes.

Examples