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 
  
# A function to print all prime factors of  
# a given number n 
def primeFactors(n): 
      
    cnt=0
    cnt1=0
    while n % 2 == 0: 
        n = n // 2
        cnt1+=1
          
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            if i%2!=0:
                cnt+=1
            else:
                cnt1+=1
            n = n // i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        if n%2!=0:
            cnt+=1
        else:
            cnt1+=1
    
    return cnt,cnt1


t=int(input())
for _ in range(t):
    n=int(input())
    if n>1:
        if n%2!=0:
            print("Ashishgup")
        else:
            x,y=primeFactors(n)
            #print(x,y)
            if (x>0 and y>1) or (x>1 and y==1) or (x==0 and y==1):
                print("Ashishgup")
            else:
                print("FastestFinger")
    else:
        print("FastestFinger")