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.
# -*- coding: utf-8 -*-
"""
Created on Mon Jun 22 23:36:40 2020

@author: Dark Soul
"""
import math
def num_odd(n):
    odd=[]
   
    for j in range(2,int(math.sqrt(n))+1,1):
        if n%j==0:
            if j%2!=0:
                odd.append(j)
            elif (n/j)%2!=0:
                odd.append(int(n/j))
    
    return odd
    
n=input('')
n=int(n)
str=[]
for i in range(n):
    str.append(int(input('')))
for k in str:
    my_num=num_odd(k)
    
    if k==1:
        print('FastestFinger')
    elif k==2 or k%2!=0:
        print('Ashishgup')
    else:
        if len(my_num)==1:
            num=my_num[0]
            if (k/num)%4==0:
                print('Ashishgup')
            else:
                print('FastestFinger')
        else:
            if len(my_num)==0:
                print('FastestFinger')
            else:
                print('Ashishgup')
    
            