Ashishgup and FastestFinger play a game. 

They start with a number n and play in turns. In each turn, a player can make any one of the following moves:

  * Divide n by any of its odd divisors greater than 1. 
  * Subtract 1 from n if n is greater than 1. 



Divisors of a number include the number itself.

The player who is unable to make a move loses the game.

Ashishgup moves first. Determine the winner of the game if both of them play optimally.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The only line of each test case contains a single integer — n (1 ≤ n ≤ 10^9).

Output

For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).

Example

Input


7
1
2
3
4
5
6
12


Output


FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup

Note

In the first test case, n = 1, Ashishgup cannot make a move. He loses.

In the second test case, n = 2, Ashishgup subtracts 1 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the third test case, n = 3, Ashishgup divides by 3 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the last test case, n = 12, Ashishgup divides it by 3. Now n = 4, FastestFinger is forced to subtract 1, and Ashishgup gets 3, so he wins by dividing it by 3.
import math

def odd_divisors(x):
    cross_section = int(math.sqrt(x))
    while cross_section > 1:
        res = x % cross_section
        if res == 0:
            foo = x // cross_section
            if foo % 2 == 1:
                yield foo
            if cross_section % 2 == 1:
                yield cross_section
        cross_section -= 1

def solve(x):
    if x == 1:
        return 1
    elif x == 2:
        return 0
    elif x == 3:
        return 0
    elif x == 4:
        return 1
    if x % 2 == 0:
        for i in odd_divisors(x):
            if x // i != 2:
                return 0
        return 1
    return 0

names = ['Ashishgup', 'FastestFinger']
T = int(input().rstrip())
for test in range(T):
    x = int(input().rstrip())
    res = solve(x)
    print(names[res])
