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 sys
import math
t=int(sys.stdin.readline())
for _ in range(t):
    n=int(input())
    if(n==1):
        print("FastestFinger")
    elif (n==2):
        print("Ashishgup")
    else:    
        if(n%2==1):
            print("Ashishgup")
        else:
            flag=True
            c=n
            while(n>1):
                if(n%2==1):
                    flag=False
                    break
                n=n//2
            if(flag):
                print("FastestFinger")
            else:
                n=c
                i = 2
                div=[]
                while(i <= math.sqrt(n)): 
                    if (n % i == 0) : 
                        # If divisors are equal, print only one 
                        if (n / i == i) : 
                            if(i%2==1):
                                div.append(i)
                        else : 
                            
                            # Otherwise print both 
                            if(i%2==1):
                                div.append(i)
                            if((n//i)%2==1):
                                
                                div.append(n//i) 
                    i = i + 1
                flag=True
                for i in range(len(div)):
                    k=n//div[i]
                    while(k>1):
                        if(k%2==1):
                            flag=False
                            break
                        k=k//2
                if(flag==True and len(div)==1 and n//div[0]==2):    
                    print("FastestFinger")
                else:
                    print("Ashishgup")
                    
                    
                    
            