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.
import sys
# sys.stdin = open('input.txt', 'r') 
# sys.stdout = open('output.txt', 'w')
 
import math
import collections
from sys import stdin,stdout,setrecursionlimit
import bisect as bs
setrecursionlimit(2**20)
M = 10**9+7

T = int(stdin.readline())
# T = 1

for _ in range(T):
    n = int(stdin.readline())
    # x,y,n = list(map(int,stdin.readline().split()))
    # a = list(map(int,stdin.readline().split()))
    # b = list(map(int,stdin.readline().split()))
    # q = list(map(int,stdin.readline().split()))
    # b = list(map(int,stdin.readline().split()))
    # s = stdin.readline().strip('\n')
    if(n == 1):
        print("FastestFinger")
        continue
    if(n == 2 or n%2 == 1):
        print("Ashishgup")
        continue
    c1 = 0
    while(n%2 == 0):
        c1 += 1
        n = n//2
    if(n == 1):
        print("FastestFinger")
        continue
    if(c1 != 1):
        print("Ashishgup")
        continue
    res = False
    for i in range(3,int(math.sqrt(n))+1,2):
        if(n%i == 0):
            res = True
            break
    if(res):
        print("Ashishgup")
    else:
        print("FastestFinger")
    