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.setrecursionlimit(2000)

def divisors(n):
    for i in range(1,n//2+1):
        if n%i == 0: 
            yield i
    yield n

def nextns(n):
    result = []
    if n > 1:
        result.append(n - 1)
    for d in divisors(n):
        if d%2==1 and d != 1:
            result.append(n//d)
    return result

import functools
@functools.lru_cache(maxsize=20000)
def dp(n):
    if n == 1:
        return False
    return any(not dp(np) for np in nextns(n))

def brute(N):
    if dp(N):
        return 'Ashishgup'
    else:
        return 'FastestFinger'

def powerOf2(n):
    return (n & (n-1) == 0) and n != 0

from math import sqrt
from itertools import count, islice
def isPrime(n):
    return n > 1 and all(n%i for i in islice(count(2), int(sqrt(n)-1)))

def soln(n):
    if powerOf2(n) and n != 2:
        return 'FastestFinger'
    if n % 2 == 0 and isPrime(n // 2):
        return 'FastestFinger'
    return 'Ashishgup'

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        
        # CHANGE
        # result = brute(n)
        result = soln(n)

        print(result)

def test():
    b = brute(3)
    # b = brute(12)
    print(b)

def randomTest():
    for n in range(1, 100001): 
        # b = brute(n)
        # if b == 'FastestFinger':
        #     print(f'n = {n}, divisors = {list(divisors(n))[1:-1]}')
        # else:
        #     print(f'    n = {n}, divisors = {list(divisors(n))[1:-1]}')
        print(n)
        b = brute(n)
        f = soln(n)
        if b != f:
            print('Broken!')
            print(b, f)
            return


main()
# test()
# randomTest()
