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 collections import defaultdict,deque
# import math

# l = list(map(int,input().split()))
# n,m=map(int,input().split())
# n=int(input())
for _ in range(int(input())):
    n=int(input())
    m=[n]
    if n%2!=0 and n!=1:
        print("Ashishgup")
        continue
    if n%2!=0:
        print("FastestFinger")
        continue
    if n==2:
        print("Ashishgup")
        continue
    c=0
    
    while n%2==0:
        n=n//2
        c+=1
    t=0
    for i in range(3,int(n**0.5)+1,2):
        while n%i==0:
            n=n//i
            t+=1
            if t>=2:
                break
            # x^=1
            # print(x)
    if n>2:
        t+=1
        
    if c>1 and t>0:
        print("Ashishgup")
        continue
    if c>1 and t==0:
        print("FastestFinger")
        continue
    if c==1 and t==1:
        print("FastestFinger")
        continue
    else:
        print("Ashishgup")
    
    

        