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.
def factorise(n):
    dic={}
    dic[2]=0
    if n%2==0:
        while n%2==0:
            if 2 in dic:
                dic[2]+=1
            n=n//2
    for i in range(3,int(n**(0.5)+1)):
        if n%i==0:
            while n%i==0:
                if i in dic:
                    dic[i]+=1
                else:
                    dic[i]=1
                n=n//i
    if n>2:
        dic[n]=1
    return dic
t=int(input())
for _ in range(t):
    n=int(input())
    if n==1:
        print('FastestFinger')
    elif n%2==1:
        print('Ashishgup')
    else:
        dic=factorise(n)
        odd_pow=0
        for i in dic:
            if i%2==1:
                odd_pow+= dic[i]
        if odd_pow>0:
            if odd_pow>1:
                    print('Ashishgup')
            else:        
                if dic[2]==1:
                    print('FastestFinger')
                else:
                    print('Ashishgup')
        else:
            if dic[2]==1:
                print('Ashishgup')
            else:
                print('FastestFinger')
            
                
        
        