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

def printDivisors(n):
    i = 1
    ct=0
    while i <= math.sqrt(n):
        if (n % i == 0):
            if (n // i == i):
                #print(i)
                if(i%2!=0 and i!=1):
                    ct+=1
            else:
                #print(i,n//i)
                if(i%2!=0 and i!=1):
                    ct+=1
                if((n//i)%2!=0 and (n//i)!=1):
                    ct+=1
        if(ct>1):
            return 0
        i = i + 1
    return 1
for _ in range(int(input())):
    t=int(input())
    if(t%2!=0):
        if(t==1):
            print("FastestFinger")
        else:
            print("Ashishgup")
    else:
        p=int(math.log(t,2))
        if(pow(2,p)==t):
            if(t==2):
                print("Ashishgup")
            else:
                print("FastestFinger")
        else:
            lk=t//2
            if(lk%2==0):
                print("Ashishgup")
            else:
                yu=printDivisors(lk)
                #print(yu)
                if(yu==0):
                    print("Ashishgup")
                else:
                    print("FastestFinger")