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.
#dt = {} for i in x: dt[i] = dt.get(i,0)+1
import sys
input = sys.stdin.readline
ipnl = lambda n: [int(input()) for _ in range(n)]
inp = lambda :int(input())
ip = lambda :[int(w) for w in input().split()]

def pfact(num):
    from math import sqrt
    dt = {}
    while num%2==0:
        dt[2] = dt.get(2,0) + 1
        num //= 2
    for i in range(3,int(sqrt(num))+1,2):
        while num%i==0:
            dt[i] = dt.get(i,0) + 1
            num //= i
    if num>2:
        dt[num] = dt.get(num,0) + 1
    return dt

for _ in range(inp()):
    n = inp()
    if n == 1:
        print("FastestFinger")
    elif n == 2 or n%2:
        print("Ashishgup")
    else:
        c = 0
        while n%2 == 0:
            n //= 2
            c += 1
        if n != 1:
            pf = pfact(n)
        else:
            pf = []
        if n == 1:
            print("FastestFinger")
        elif c > 1 or sum(list(pf.values())) >= 2:
            print("Ashishgup")
        else:
            print("FastestFinger")
            
            
            

            