Fate to hate#2850
Ira's birthday was approaching. On the night from 27th to the 28th, Sasha could not sleep for a long time. Mathematically logical nonsense was coming to mind. An ordinary daisy divination had become a cruel game of numbers and bitwise operations.
The dream was about an infinite field of indistinguishable daisies. Each daisy had petals, and each petal had a number on it. From time to time, the fear that Ira could change her ICQ number would force Sasha to wake up in a cold sweat. Every time a new number came to mind, it certainly had to be obtained from the petals by applying bitwise and operations to the numbers on them. If the number could be obtained, it was a good sign; otherwise, the dream became filled with horror and hate.
All daisies are the same, and Sasha can pick as many as needed to use these petals. To obtain a number, any non-empty subset of petals from any number of daisies can be chosen. In the dream, Sasha can fully control the order of applying the operations.
The first line contains the number — the number of petals on a daisy (1 \leq N \leq 10^5). The second line contains the integers a_i — the numbers on the petals (0 \leq a_i \leq 10^9). The next line contains the number — the number of ICQ numbers to obtain (1 \leq Q \leq 10^5). The following lines each contain one integer b_i (0 \leq b_i \leq 10^9).
For each ICQ number, output one line containing "Fate" if this number can be obtained from the numbers on the petals by applying bitwise and operations, or "Hate" if it is impossible.
1-nji mysal