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
l=[]
i=4
while(i<1000000007):
    l.append(i)
    i*=2
def printDivisors(n) : 
    i = 1
    ct=0  
    b=int(math.sqrt(n))
    for i in range(2,b+1): 
        if n%i == 0: 
            if (n // i == i) : 
                if i%2 != 0:ct+=1
            else : 
                if i%2 !=0:ct+=1
                if ((n//i)%2) != 0:ct+=1
        i = i + 1  
    return ct
for _ in range(int(input())):
    n=int(input())
    ct=printDivisors(n)
    if n==1:
        print("FastestFinger")
    elif (n==2) or (n%2 != 0):
        print("Ashishgup")
    elif n%2 == 0:
        if n in l:
            print("FastestFinger")
        elif ct==1 and n%4 != 0:
            print("FastestFinger")
        elif ct==1 and n%4==0:
            print("Ashishgup")
        elif ct>1:
            print("Ashishgup")
        