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 functools import reduce
import sys
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def factors(n):
    x=set(reduce(list.__add__,([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
    return(list(x))
l1=[]
for i in range(1,30):
    l1.append(1<<i)
#print(l1)
t=int(input())
for i in range(t):
    n=int(input())
    if n==2:
        sys.stdout.write('Ashishgup'+'\n')
    elif n==1:
        sys.stdout.write('FastestFinger'+'\n')
    elif n&1:
        sys.stdout.write('Ashishgup'+'\n')
    elif n in l1:
        sys.stdout.write('FastestFinger'+'\n')
    else:
        ok1,ok2,ok3=False,False,False
        l=factors(n)
        #print(l)
        odd=0
        for i in l:
            if i%2==1 and i!=1:
                if n//i in l1:
                    if n//i!=2:
                        ok1=True
                    else:
                        ok3=True
                else:
                    ok2=True
        if ok1==True or ok2==True:
            sys.stdout.write("Ashishgup"+'\n')
        elif ok3==True:
            sys.stdout.write('FastestFinger'+'\n')
        
              

