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 ceil
# primes = [True] * ceil(10 ** 4.5) # would floor but using 1-based indices
# # mark 2 last
# primes[2] = True
# for i in range(2, len(primes)):
# 	if not primes[i]:
# 		continue
# 	for j in range(2*i, len(primes), i):
# 		primes[j] = False
# primes = [i for i in range(3, len(primes)) if primes[i]]
for _ in range(int(input())):
	n = int(input())
	if n == 1:
		print('FastestFinger')
	elif n == 2:
		print('Ashishgup')
	# elif n / 2 % 2 == 1:
	# 	print('FastestFinger')
	elif n % 2 == 1:
		print('Ashishgup')
	else:
		# count number of odd prime factors
		# count = 0
		# for p in primes:
		# 	while n % p == 0:
		# 		n /= p
		# 		count += 1
		# count == 0 when n is power of 2
		# print(n, count)
		count = 0
		while n % 2 == 0:
			n /= 2
			count += 1
		if n == 1:
			print('FastestFinger')
		elif count > 1:
			print('Ashishgup')
		else:
			prime = True
			for x in range(3, int(n ** 0.5)+1):
				if n % x == 0:
					prime = False
					break
			if prime:
				print('FastestFinger')
			else:
				print('Ashishgup')

		# if count == 1 and n is not prime
		# or if count > 1
		# if count >= 1 and n > 2 or count > 1 and n == 2:
		# 	print('Ashishgup')
		# else:
		# 	print('FastestFinger')