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 os,io
from sys import stdout
import collections
import random
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

def binomial_coefficient(n, k):
    if 0 <= k <= n:
        ntok = 1
        ktok = 1
        for t in range(1, min(k, n - k) + 1):
            ntok *= n
            ktok *= t
            n -= 1
        return ntok // ktok
    else:
        return 0

def powerOfK(k, max):
    if k == 1:
        return [1]
    if k == -1:
        return [-1, 1]

    result = []
    n = 1
    while n <= max:
        result.append(n)
        n *= k
    return result

def prefixSum(arr):
    for i in range(1, len(arr)):
        arr[i] = arr[i] + arr[i-1]
    return arr

def divisors(n):
    i = 1
    result = []
    while i*i <= n:
        if n%i == 0:
            if n/i == i:
                result.append(i)
            else:
                result.append(i)
                result.append(n/i)
        i+=1
    return result

memo_divs = {}

def solve(n, p):
    if n == 1:
        return not p
    if n == 2:
        return p

    if n in memo_divs:
        divs = memo_divs[n]
    else:
        divs = list(filter(lambda x: x % 2 == 1 and x > 1, divisors(n)))
        memo_divs[n] = divs

    if not len(divs):
        return not p
    else:
        for d in divs:
            if solve(int(n//d), not p) == p:
                return p
        return not p

t = int(input())
for _ in range(t):
    n = int(input())
    if n == 1:
        print("FastestFinger")
    elif n % 2 == 1:
        print("Ashishgup")
    else:
        r = solve(n, True)
        if r:
            print("Ashishgup")
        else:
            print("FastestFinger")
