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 copy import *
from math import *

def printDivisors(n) : 
    l=[]
    # Note that this loop runs till square root 
    i = 1
    while i <= sqrt(n): 
          
        if (n % i == 0) : 
              
            # If divisors are equal, print only one 
            if (n / i == i) : 
                l.append(i)
            else : 
                # Otherwise print both 
                l.extend([i , n//i]) 

        i = i + 1
    return l


# print(sorted(printDivisors(99804)))
t=int(input())
for i in range(t):
    n=int(input())
    # l=list(map(int,input().split()))
    if n==1:
        print("FastestFinger")
        continue
    if n%2==1 or n==2:
        print("Ashishgup")
        continue
    if n==4 or n==6:
        print("FastestFinger")
        continue
    
    
    
    kk=printDivisors(n)
    kk.sort()
    kk=deepcopy(kk[1:])
    kk=sorted(kk,reverse=True)
    # print(kk)
    val=False
    for j in range(len(kk)):
        if kk[j]%2==1:
            FET=n//kk[j]
            if FET!=2:
                val=True
                break
    if val==False:
        print("FastestFinger")

    
    # if val==0:
    #     print("FastestFinger")
    #     continue
    # else:
    #     print(n,val,n//val)
    #     DAD=n//val
    #     if DAD==2:
    #         print("FastestFinger")
    #     else:
    #     # c=log(DAD,2)
    #     # if c%2==0:
    #         print("Ashishgup")

    else:
        print("Ashishgup")



