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.
from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,gcd
for _ in range(int(input())):
	n=int(input())
	l=[]
	x=n
	a=2
	ans=["Ashishgup","FastestFinger"]
	if n>1:
		while x>1 and a<=sqrt(n):
			if x%a==0:
				l.append(a)
				x=x//a
			else:
				a+=1
		if x>1:
			l.append(x)
		a=0
		while n>1:
			if n%2!=0:
				break
			else:
				if len(l)>0:
					z=1
					e=[]
					t=1
					for i in l:
						if i%2==0:
							e.append(i)
						else:
							z*=i
							t=i
					if z==1:
						n-=1
						a+=1
						break
					else:
						if len(e)>1:
							n=n//z
							l=list(e)
						else:
							z=z//t
							if z>1:
								n=n//z
								l=list(e)
								l.append(t)
							else:
								n=n//t
								l=list(e)

				else:
					n-=1
					a+=1
					break
			a+=1
		if n!=1:
			print(ans[a%2])
		else:
			print(ans[(a+1)%2])
 
	else:
		print(ans[1])