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.


t = int(input())
while t!=0:

    n = int(input())
    if n%2==0:
        count=0
        f2=0
        while n%2==0:
            f1=0
            maxi=-1
            for i in range(3,int(pow(n,.5)+1)):
                if n%i==0:
                    if i%2==1:
                        if i>maxi:
                            maxi=i
                    if (n//i) %2==1:
                        if (n//i) >maxi:
                            maxi=n//i

            if maxi!=-1:
                
                n = n//maxi

                count+=1
                f1=1

            if n==2:
                f2=1

            if f1==0:
                n-=1

                count+=1

        if f2==1:
            if count % 2 == 1:
                print("Ashishgup")
            else:
                print("FastestFinger")
        else:

            if count%2==1:
                print("FastestFinger")
            else:
                print("Ashishgup")



    else:
        if n==1:
            print("FastestFinger")
        else:
            print("Ashishgup")
    t-=1