Fate to hate

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 discretely coming to the head. An ordinary daisy divination has become a cruel game of numbers and bit operations.

The dream was about an infinite field of indistinguishable daisies. Each daisy had N petals, and each of them had a number on it. From time to time, the fear that Ira can change the number of her ICQ forced to wake up in a cold sweat. And every time a new number came to head, it certainly had to be obtained from the petals by applying to the numbers written on them operations, AND and OR. If the number could be obtained, it was a good sign, otherwise the same dream became infused with horror of hate and evil.

All daisies are the same, and they can be endlessly to picked in order to use the right petals. So to get one number, you can pick several daisies and pick a non-empty subset of their petals. In his dreams, Sasha is able to fully control the order of operations.

Input

The first line contains the number N — the number of petals on a daisy (1 ≤ N ≤ 10^5). The next line lists the integers on the petals a_i (0 ≤ a_i ≤ 10^9). Next line contains the number Q — the number of ICQ-numbers which must be obtained (1 ≤ Q ≤ 10^5). Each of the following Q lines contains one ICQ number b_i (0 ≤ b_i ≤ 10^9).

Output

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 and OR, operations to them, or "Hate", if it is impossible.

Examples