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.
def isPrime(n,i) : 
    if (n <= 1) :return False
    if (n <= 3) :return True
    if (n % 2 == 0 or n % 3 == 0) :return False  
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) :return False
        i += 6  
    return True
for _ in range(int(input())):
    n,k = int(input()),0
    if n == 1:ans = 2
    if n == 2:ans = 1
    if n > 2:
        if n % 2 == 1:ans = 1
        else:
            while n % 2 == 0:k += 1;n //= 2
            if n == 1 and k > 1:ans = 2
            if n > 1 and k == 1:ans = (2 if isPrime(n,5) == True else 1)
            if n > 1 and k > 1:ans = 1        
    print("Ashishgup") if ans == 1 else print("FastestFinger")    