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
J=lambda : int(input())
def get_factors(n):
    ans=set()
    for i in range(1,int(math.sqrt(n))+1):
        if n%i==0:
            if i!=1:
                if i%2==1:
                    ans.add(i)
                if (n//i)%2==1:
                    ans.add(n//i)
    return list(ans)


dct={1:0,2:1}
def getAns(n):
    if n in dct:
        return dct[n]
    if n%2==1:
        return 1
    else:
        if 0 in [getAns(n//fac) for fac in get_factors(n)]:
            dct[n]=1
            return dct[n]
        else:
            dct[n]=0
            return 0
        
for _ in range(J()):
    n=J()
    if getAns(n)==1:
        print('Ashishgup')
    else:
        print('FastestFinger')