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 
  
import math 
  
# A function to print all prime factors of  
# a given number n 
def pr(n): 
    a=[]
    # Print the number of two's that divide n 
    while n % 2 == 0: 
        a.append(2) 
        n = n / 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            a.append(int(i)) 
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        a.append(int(n))
    return a
          
# Driver Program to test above function 


import math as ma
# import sys
# input=sys.stdin.readline

t=int(input())
for _ in range(t):
    n=int(input())
    aa=["Ashishgup","FastestFinger"]
    if n==1:
        print(aa[1])
    elif n==2:
        print(aa[0])
    elif n%2!=0:
        print(aa[0])
    else:
        c=0
        while 1>0:
            if n%2==0:
                n=n//2
                c+=1
            else:
                break
        if n==1:
            print(aa[1])
        elif c==1:
            a=pr(n)
            b=0
            for i in range(len(a)):
                if a[i]%2!=0:
                    b+=1
            if b>1:
                print(aa[0])
            else:
                print(aa[1])
        else:
            print(aa[0])