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.
#!/usr/bin/env python3
import io
import os

input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

def get_str():
    return input().decode().strip()

def rint():
    return map(int, input().split())

def oint():
    return int(input())

def max_odd_div(n):
    while n%2 == 0:
        n //= 2
    return n

def find_min_div(n):
    i = 2
    while i*i <= n:
        if n % i == 0:
            return i
        i += 1
    return 1

name = ['FastestFinger', 'Ashishgup']
t = oint()

for _ in range(t):
    n = oint()
    turn = 0
    while True:
        if n == 1:
            break
        max_od =  max_odd_div(n)
        if max_od > 1:
            if n // max_od == 2:
                min_div = find_min_div(max_od)
                n //= max_od//min_div
                turn += 1
            else:
                n //= max_od
                turn += 1
        else:
            n -= 1
            turn += 1
    print(name[turn%2])
