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 math import sqrt, ceil
MAX = 10**9

def getPrimeFactors(n):
	nums = [0]*ceil(sqrt(n))
	nums[0] = 1
	nums[1] = 1
	for i in range(2, ceil(sqrt(sqrt(n)))):
		if not nums[i]:
			for j in range(i*i, ceil(sqrt(n)), i):
				nums[j] = 1
	return [i for i, x in enumerate(nums) if not x]

factors = getPrimeFactors(MAX)

def isPrime(n):
	for f in factors:
		if n%f == 0:
			return False
	return True

def numOddPowers(n):
	while n%2 == 0:
		n /= 2

	if n in factors:
		return 1
	else:
		count = 0
		for p in factors:
			if n < p:
				break
			if n%p == 0:
				while n%p == 0:
					n /= p
					count += 1
		if isPrime(n):
			count += 1
	return count


t = int(input())
for _ in range(t):
	n = int(input())
	if n == 1:
		print('FastestFinger')
	elif n == 2:
		print('Ashishgup')
	elif n & n-1 == 0:
		print('FastestFinger')
	elif n%2:
		print('Ashishgup')
	elif (n/2)%2:
		#even with one 2 and some odds
		if numOddPowers(n) > 1:
			print('Ashishgup')
		else:
			print('FastestFinger')
	else:
		#even with more than one 2s
		print('Ashishgup')
