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.
# -*- coding: utf-8 -*-
import math, string, itertools, operator, fractions, heapq, collections, re, array, bisect, sys, functools
def solve(line):
    n = int(line)
    if n == 1: return "FastestFinger"
    if n == 2: return "Ashishgup"
    if n % 2 == 1: return "Ashishgup"
    cn = []
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0 and (i % 2 == 1 or (n // i) % 2 == 1):
            if i % 2 == 1: cn.append(i)
            else: cn.append(n // i)
            if len(cn) > 1:
                break
    if len(cn) == 0: return "FastestFinger"
    if len(cn) == 1: return "FastestFinger" if (n // 2) % 2 == 1 else "Ashishgup"
    return "Ashishgup"
    
T = int(sys.stdin.readline())
t = 0
while True:
    line = sys.stdin.readline().rstrip()
    if not line:
        break
    print(solve(line))
    t += 1
