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.
from math import sqrt
def get_Divisors(n) :
    arr=[]
    i = 1
    while i <= sqrt(n):
        if (n % i == 0) :
            if (n / i == i) :
                arr.append(i)
            else :
                arr.append(i)
                arr.append(n//i)
        i = i + 1
    arr.sort()
    res=[]
    for item in arr:
        if item>1 and item%2:
            res.append(item)
    return res

def isprime(n):
    i=2 
    while(i*i<=n):
        if(n%i==0):
            return 0
        i+=1 
    return 1
for ttt in range (int(input())):
    n=int(input())
    if(n==1):
        print("FastestFinger")
        continue
    if(n==2):
        print("Ashishgup")
        continue
    if(n%2):
        print("Ashishgup")
    else:
        x=n
        res=get_Divisors(n)
        if(len(res)):
            x//=res[0]
            if(x>2):
                print("Ashishgup")
            else:
                print("FastestFinger")    
        else:    
            print("FastestFinger")