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 functools import lru_cache
from sys import stdin, stdout
import sys
from math import *
# sys.setrecursionlimit(3*int(1e5))
# input = stdin.buffer.readline
# print = stdout.write
 
# @lru_cache()

def fec(n):
	f=[]
	for i in range(2,int(sqrt(n))+1):
		if(n%i==0):
			if(n%(n//i)==0 and (n//i)%2==1 and (n//(n//i))%2==0):
				f.append(n//i)
			if(i%2==1 and (n//i)%2==0):
				f.append(i)
	f.sort()
	return f

for __ in range(int(input())):
	n=int(input())
	if(n==1):
		print("FastestFinger")
	elif(n%2==1 or n==2):
		print("Ashishgup")
	else:
		# print(fec(n))
		t=0
		# if(n%4==0 and (n//4)%2==1 and n>4):
			# t=1
		f=fec(n)
		if(len(f)==0):
			print("FastestFinger")
		else:
			if(len(f)==1 and (n//f[0])%2==1 or n//f[0]==2):
				print("FastestFinger")
			else:
				print("Ashishgup")
		
