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
input = sys.stdin.readline
#Ashishgup moves first

def win():
    print('Ashishgup')
def lose():
    print('FastestFinger')

def isprime(n):
    for i in range(2, min(50000, n)):
        if n % i == 0:
            return False
    return True

for _ in range(int(input())):
    n = int(input())
    if n == 1:
        lose()
    elif n == 2:
        win()
    elif n % 2 != 0: # odd
        win()
    else: # even
        #n % 2 == 0:            
        #2^n(lose) 
        #2*p(lose - p is prime), 2*p'*odd(win - p not prime)   
        #4*odd(win)
        n = n//2
        if n%2 != 0: # 2*p(lose) / 2*p'*odd(win)
            if isprime(n):
                lose()
            else:
                win()
        else: # 2^n / 4*odd
            while n%2 == 0: n = n//2
            if n == 1: lose()
            else: win()
