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,math

_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__

def if2pow(n):
	for i in range(1,33):
		if(2**i == n):
			return True 
		if(2**i > n):
			return False 
	return False

def isPrim(n):
	p = int(math.sqrt(n))+1 
	ans = True 
	for i in range(2,p+1):
		if(n % i == 0):
			ans = False 
			break
	return ans 

isPrime = [True]*100001

isPrime[0] = isPrime[1] = False 

b = int(math.sqrt(10001)+2)

for i in range(2,b) :
	if isPrime[i] :
		for j in range(i*i,100001,i):
			isPrime[j] = False 

tc = int(input()) 

for zzz in range(tc):
	n = int(input()) 
	ans = ""

	if(n == 1):
		ans = "FastestFinger"
	elif(n % 2 == 1 or n == 2) :
		ans = "Ashishgup"
	else :
		if(if2pow(n)):
			ans = "FastestFinger"
		else:
			n //= 2 
			if(isPrim(n)) :
				ans = "FastestFinger"
			else:
				ans = "Ashishgup"
	print(ans)
