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 sys
import math

t = int(sys.stdin.readline().strip())
for _ in range(t):
	n = int(sys.stdin.readline().strip())
	if n == 1:
		print("FastestFinger")
	else:
		if n % 2 == 1:
			print("Ashishgup")
		else:
			odds = 0
			twos = 0
			x = n
			while n % 2 == 0:
				twos += 1
				n  = n / 2
			for i in range(3,int(math.sqrt(n))+1,2): 
				while n % i == 0: 
					odds += 1
					n = n / i
			if n > 1:
				odds += 1
			
			if x == 2:
				print("Ashishgup")
			else:
				if odds > 0:
					if odds == 1 and twos == 1:
						print("FastestFinger")
					else:
						print("Ashishgup")
				else:
					print("FastestFinger")




def primeFactors(n): 
	  
	# Print the number of two's that divide n 
	while n % 2 == 0: 
		print 2, 
		n = n / 2
		  
	# n must be odd at this point 
	# so a skip of 2 ( i = i + 2) can be used 
	for i in range(3,int(math.sqrt(n))+1,2): 
		  
		# while i divides n , print i ad divide n 
		while n % i== 0: 
			print i, 
			n = n / i 