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.
# Author: S Mahesh Raju
# Username: maheshraju2020
# Date: 20/06/2020

from sys import stdin,stdout
from math import gcd, ceil, sqrt
ii1 = lambda: int(stdin.readline().strip())
is1 = lambda: stdin.readline().strip()
iia = lambda: list(map(int, stdin.readline().strip().split()))
isa = lambda: stdin.readline().strip().split()
mod = 1000000007

def divisors(num):
    temp = set([1])
    for i in range(1, int(num ** 0.5) + 1):
        if num % i == 0:
            if i % 2 != 0 and num // i != 2:
                temp.add(i)
            if (num // i) % 2 != 0 and i!=2:
                temp.add(num // i)
    return max(temp)


tc = ii1()
for i in range(tc):
    n = ii1()
    if n == 1:
        print("FastestFinger")
    elif n % 2 != 0:
        print("Ashishgup")
    elif n == 2:
        print("Ashishgup")
    else:
        flip = False
        while True:
            cur = divisors(n)
            if cur == 1:
                break
            n = n // cur
            flip = True if not flip else False
        else:
            break
        if flip:
            print("Ashishgup")
        else:
            print("FastestFinger")



        
