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.
"""
Created on Fri May  1 20:20:46 2020

@author: sofianeLewin
"""
prime_list = []
tab = [0]*100001
for i in range(2, 100001):
    if(not tab[i]):
        prime_list.append(i)
        for j in range(1, int(100001/i)):
            tab[j*i] = 1



t = int(input())
for _ in range(t):
    n = int(input())
    m = n
    name1 = "Ashishgup"
    name2 = "FastestFinger"
    if(n == 1):
        print(name2)
    elif(n == 2 or n%2):
        print(name1)
    else:
        while(not n%2):
            n = n/2
        if(n == 1):
            print(name2)
        else:
            if(m/n == 2):
                ans = 0
                for i in range(len(prime_list)):
                    if(not n%prime_list[i] and n!= prime_list[i]):
                        ans = 1
                        break
                    if(prime_list[i]>n):
                        break
                if(ans):
                    print(name1)
                else:
                    print(name2)
                # print(n)
            else:
                print(name1)
                # print(n)