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.
T = int(input())
for i in range(0, T):
	flag = 0
	n = int(input())
	while True:
		if n == 1:
			flag += 1
			break
		elif n%2==1:
			break
		else:
			if n == 2:
				break;
			else:
				tar = n
				mark = 0
				l1_div = 1
				for j in range(2, int(pow(tar, 0.5))+1):
					# print(j)
					if tar%j == 0:
						if j%2!= 0:
							mark = 1
							if l1_div<j:
								l1_div = j
								# print("ll", div)	
						else:
							tar2 = int(tar//j)
							# print(tar2)
							if tar2%2!=0:
								mark = 1
								if l1_div < tar2:
									l1_div = tar2
									# print("ll", div)
				mark_1 = 0
				l2_div = 1
				for j in range(2, int(pow(tar, 0.5))+1):
					# print(j)
					if tar%j == 0:
						if j%2!= 0:
							mark_1 = 1
							if l2_div<j and j!=l1_div:
								l2_div = j
								# print("ll", div)	
						else:
							tar2 = int(tar//j)
							# print(tar2)
							if tar2%2!=0:
								mark_1 = 1
								if l2_div < tar2 and tar2 !=l1_div:
									l2_div = tar2
									# print("ll", div)
								
				# print(mark)
				if l1_div == 1:
					mark = 0
				if l2_div == 1:
					mark_1 = 0
				# print(l1_div, l2_div)
				if mark_1 == 1:
					if n//l1_div == 2:
						n = n//l2_div
						flag +=1
					else:
						n = n//l1_div
						flag += 1
				elif mark_1 == 0 and mark == 1:
					n = n//l1_div
					flag += 1 
				else:
					flag += 1
					break
	if flag%2 == 0:
		print("Ashishgup")
	else:
		print("FastestFinger")
