human
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.
 ... Give me a Python code to determine the winner of the game if both of them play optimally?
assistant
#Here is Python code to determine the winner of the game if both of them play optimally.

# f = open('test.py')
# def input():
# 	return f.readline().replace('\n','')

import math

def read_list():
	return list(map(int,input().strip().split(' ')))
def print_list(l):
	print(' '.join(map(str,l)))
N = int(input())
for _ in range(N):
	n = int(input())
	if n==1:
		print('FastestFinger')
	elif n&1 or n==2:
		print('Ashishgup')
	else:
		if (n>>1)&1==0:
			while n:
				if n&1==1:
					break 
				n>>=1				
			if n>1:
				print('Ashishgup')
			else:
				print('FastestFinger')

		else:
			n>>=1
			flag = False
			key = int(math.sqrt(n))
			if key*key==n:
				flag=True
			else:
				i = 3
				while i<=key:
					if n%i==0:
						flag = True
						break
					i+=2
			if flag:
				print('Ashishgup')
			else:		
				print('FastestFinger')