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 math 
def prime(n): 
    while n % 2 == 0: 
        lis.append(2)
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            lis.append(i)
            n = n / i 
    if n > 2: 
        lis.append(n)
for _ in range(int(input())):
    lis=[]
    n = int(input())
    if n==1:
        print("FastestFinger")
    elif n==2:
        print("Ashishgup")    
    elif n%2!=0:
        print("Ashishgup")
    else:
        prime(n)
        c=0
        c1=0
        for i in lis:
            if i%2==0:
                c+=1
            else:
                c1+=1
        if  c>1 and c1>0:
            print("Ashishgup") 
        elif c==1 and c1>1:
            print("Ashishgup") 
        else:
            print("FastestFinger")                  





